diff --git a/.github/workflows/gh-pages.yml b/.github/workflows/gh-pages.yml
new file mode 100644
index 00000000000..ad9b0943d4f
--- /dev/null
+++ b/.github/workflows/gh-pages.yml
@@ -0,0 +1,29 @@
+name: gh-pages
+
+on:
+  push:
+    branches:
+      - master
+
+jobs:
+  deploy:
+    name: GH-pages documentation
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install toolchain
+        uses: actions-rs/toolchain@v1
+        with:
+          profile: minimal
+          toolchain: nightly
+          override: true
+      - name: doc (rand)
+        env:
+          RUSTDOCFLAGS: --cfg doc_cfg
+        # --all builds all crates, but with default features for other crates (okay in this case)
+        run: cargo doc --all --features nightly,serde1,getrandom,small_rng
+      - name: Deploy
+        uses: peaceiris/actions-gh-pages@v3
+        with:
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          publish_dir: ./target/doc
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
new file mode 100644
index 00000000000..686cea4baaf
--- /dev/null
+++ b/.github/workflows/test.yml
@@ -0,0 +1,185 @@
+name: Tests
+
+on:
+  push:
+    branches: [ master, '0.[0-9]+' ]
+  pull_request:
+    branches: [ master, '0.[0-9]+' ]
+
+jobs:
+  check-doc:
+    name: Check doc
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install toolchain
+        uses: actions-rs/toolchain@v1
+        with:
+          profile: minimal
+          toolchain: nightly
+          override: true
+      - run: cargo install cargo-deadlinks
+      - name: doc (rand)
+        env:
+          RUSTDOCFLAGS: --cfg doc_cfg
+        # --all builds all crates, but with default features for other crates (okay in this case)
+        run: cargo deadlinks --ignore-fragments -- --all --features nightly,serde1,getrandom,small_rng
+
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - os: ubuntu-latest
+            target: x86_64-unknown-linux-gnu
+            toolchain: stable
+          - os: macos-latest
+            target: x86_64-apple-darwin
+            toolchain: stable
+            # TODO: also aarch64 / M1
+          - os: windows-latest
+            target: x86_64-pc-windows-gnu
+            toolchain: stable
+          - os: windows-latest
+            target: x86_64-pc-windows-msvc
+            toolchain: beta
+            # Test both windows-gnu and windows-msvc; use beta rust on one
+          - os: ubuntu-latest
+            target: x86_64-unknown-linux-gnu
+            toolchain: 1.36.0 # MSRV
+          - os: ubuntu-latest
+            deps: sudo apt install gcc-multilib
+            target: i686-unknown-linux-gnu
+            toolchain: nightly
+          - os: ubuntu-latest
+            target: x86_64-unknown-linux-gnu
+            toolchain: nightly
+            variant: minimal
+
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install toolchain
+        uses: actions-rs/toolchain@v1
+        with:
+          profile: minimal
+          target: ${{ matrix.target }}
+          toolchain: ${{ matrix.toolchain }}
+          override: true
+      - run: ${{ matrix.deps }}
+      - name: Maybe minimal
+        if: ${{ matrix.variant == 'minimal' }}
+        run: cargo generate-lockfile -Z minimal-versions
+      - name: Maybe nightly
+        if: ${{ matrix.toolchain == 'nightly' }}
+        run: |
+          cargo test --target ${{ matrix.target }} --tests --features=nightly
+          cargo test --target ${{ matrix.target }} --all-features
+          cargo test --target ${{ matrix.target }} --benches --features=nightly
+          cargo test --target ${{ matrix.target }} --manifest-path rand_distr/Cargo.toml --benches
+      - name: Test rand
+        run: |
+          cargo test --target ${{ matrix.target }} --tests --no-default-features
+          cargo test --target ${{ matrix.target }} --tests --no-default-features --features=alloc,getrandom,small_rng
+          # all stable features:
+          cargo test --target ${{ matrix.target }} --features=serde1,log,small_rng
+          cargo test --target ${{ matrix.target }} --examples
+      - name: Test rand_core
+        run: |
+          cargo test --target ${{ matrix.target }} --manifest-path rand_core/Cargo.toml
+          cargo test --target ${{ matrix.target }} --manifest-path rand_core/Cargo.toml --no-default-features
+          cargo test --target ${{ matrix.target }} --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc,getrandom
+      - name: Test rand_distr
+        run: cargo test --target ${{ matrix.target }} --manifest-path rand_distr/Cargo.toml
+      - name: Test rand_pcg
+        run: cargo test --target ${{ matrix.target }} --manifest-path rand_pcg/Cargo.toml --features=serde1
+      - name: Test rand_chacha
+        run: cargo test --target ${{ matrix.target }} --manifest-path rand_chacha/Cargo.toml
+      - name: Test rand_hc
+        run: cargo test --target ${{ matrix.target }} --manifest-path rand_hc/Cargo.toml
+
+  test-cross:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - os: ubuntu-latest
+            target: mips-unknown-linux-gnu
+            toolchain: stable
+
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install toolchain
+        uses: actions-rs/toolchain@v1
+        with:
+          profile: minimal
+          target: ${{ matrix.target }}
+          toolchain: ${{ matrix.toolchain }}
+          override: true
+      - name: Cache cargo plugins
+        uses: actions/cache@v1
+        with:
+          path: ~/.cargo/bin/
+          key: ${{ runner.os }}-cargo-plugins
+      - name: Install cross
+        run: cargo install cross || true
+      - name: Test
+        run: |
+          # all stable features:
+          cross test --no-fail-fast --target ${{ matrix.target }} --features=serde1,log,small_rng
+          cross test --no-fail-fast --target ${{ matrix.target }} --examples
+          cross test --no-fail-fast --target ${{ matrix.target }} --manifest-path rand_core/Cargo.toml
+          cross test --no-fail-fast --target ${{ matrix.target }} --manifest-path rand_distr/Cargo.toml
+          cross test --no-fail-fast --target ${{ matrix.target }} --manifest-path rand_pcg/Cargo.toml --features=serde1
+          cross test --no-fail-fast --target ${{ matrix.target }} --manifest-path rand_chacha/Cargo.toml
+          cross test --no-fail-fast --target ${{ matrix.target }} --manifest-path rand_hc/Cargo.toml
+
+  test-miri:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install toolchain
+        run: |
+          MIRI_NIGHTLY=nightly-$(curl -s https://rust-lang.github.io/rustup-components-history/x86_64-unknown-linux-gnu/miri)
+          rustup default "$MIRI_NIGHTLY"
+          rustup component add miri
+      - name: Test rand
+        run: |
+          cargo miri test --no-default-features
+          cargo miri test --features=log,small_rng
+          cargo miri test --manifest-path rand_core/Cargo.toml
+          cargo miri test --manifest-path rand_core/Cargo.toml --features=serde1
+          cargo miri test --manifest-path rand_core/Cargo.toml --no-default-features
+          #cargo miri test --manifest-path rand_distr/Cargo.toml # no unsafe and lots of slow tests
+          cargo miri test --manifest-path rand_pcg/Cargo.toml --features=serde1
+          cargo miri test --manifest-path rand_chacha/Cargo.toml --no-default-features
+          cargo miri test --manifest-path rand_hc/Cargo.toml
+
+  test-no-std:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install toolchain
+        uses: actions-rs/toolchain@v1
+        with:
+            profile: minimal
+            toolchain: nightly
+            target: thumbv6m-none-eabi
+            override: true
+      - name: Build top-level only
+        run: cargo build --target=thumbv6m-none-eabi --no-default-features
+
+  test-ios:
+    runs-on: macos-latest
+    steps:
+      - uses: actions/checkout@v2
+      - name: Install toolchain
+        uses: actions-rs/toolchain@v1
+        with:
+            profile: minimal
+            toolchain: nightly
+            target: aarch64-apple-ios
+            override: true
+      - name: Build top-level only
+        run: cargo build --target=aarch64-apple-ios
diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index 35d755e3527..00000000000
--- a/.travis.yml
+++ /dev/null
@@ -1,115 +0,0 @@
-language: rust
-sudo: false
-
-# Since most OS-specific code has moved to the getrandom crate, we require
-# few target-specific tests here.
-
-matrix:
-  include:
-    - rust: 1.36.0
-      name: "Linux, 1.36.0"
-      os: linux
-
-    - rust: stable
-      name: "Linux, stable"
-
-    - rust: stable
-      name: "OSX+iOS, stable"
-      os: osx
-      install:
-        - rustup target add aarch64-apple-ios
-      script:
-        - bash utils/ci/script.sh
-        - cargo build --target=aarch64-apple-ios
-
-    - rust: beta
-      name: "Linux, beta"
-
-    - rust: nightly
-      os: linux
-      name: "Linux, nightly, docs"
-      env: NIGHTLY=1
-      install:
-        - cargo --list | egrep "^\s*deadlinks$" -q || cargo install cargo-deadlinks
-        - cargo deadlinks -V
-      before_script:
-        - pip install 'travis-cargo<0.2' --user && export PATH=$HOME/.local/bin:$PATH
-      script:
-        - bash utils/ci/script.sh
-        # remove cached documentation, otherwise files from previous PRs can get included
-        - rm -rf target/doc
-        - cargo doc --no-deps --all --all-features
-        - cargo deadlinks --dir target/doc
-      deploy:
-        local_dir: target/doc
-        provider: pages
-        skip_cleanup: true
-        github_token: $GITHUB_TOKEN
-        on:
-          branch: master
-
-    # This target catches endianness issues
-    - rust: stable
-      sudo: required
-      dist: trusty
-      services: docker
-      name: "Linux (MIPS, big-endian)"
-      env: TARGET=mips-unknown-linux-gnu
-      install:
-        - sh utils/ci/install.sh
-        - source ~/.cargo/env || true
-
-    # This target checks we really can build no_std binaries
-    - rust: nightly
-      name: "no_std platform test"
-      install:
-        - rustup target add thumbv6m-none-eabi
-      script:
-        # Test the top-level crate with all features:
-        - cargo build --target=thumbv6m-none-eabi --no-default-features
-
-    - rust: nightly
-      name: "Linux, nightly (32-bit test)"
-      env: TARGET=i686-unknown-linux-musl
-      install:
-        - rustup target add $TARGET
-
-    - rust: nightly
-      os: linux
-      name: "Miri, nightly"
-      script:
-        - sh utils/ci/miri.sh
-    
-    - rust: nightly
-      os: linux
-      name: "Minimal dep versions"
-      script:
-        - cargo generate-lockfile -Z minimal-versions
-        - bash utils/ci/script.sh
-
-before_install:
-  - set -e
-  - rustup self update
-
-script:
-  - bash utils/ci/script.sh
-
-after_script: set +e
-
-# Cache: this seems to do more harm than good
-#cache:
-  #cargo: true
-  #directories:
-    #- .local/share/cargo-web
-
-#before_cache:
-  ## Travis can't cache files that are not readable by "others"
-  #- chmod -R a+r $HOME/.cargo
-
-env:
-  global:
-    secure: "BdDntVHSompN+Qxz5Rz45VI4ZqhD72r6aPl166FADlnkIwS6N6FLWdqs51O7G5CpoMXEDvyYrjmRMZe/GYLIG9cmqmn/wUrWPO+PauGiIuG/D2dmfuUNvSTRcIe7UQLXrfP3yyfZPgqsH6pSnNEVopquQKy3KjzqepgriOJtbyY="
-
-notifications:
-  email:
-    on_success: never
diff --git a/Cargo.toml b/Cargo.toml
index 9284f3084fd..b6e87bab282 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -16,10 +16,6 @@ autobenches = true
 edition = "2018"
 include = ["src/", "LICENSE-*", "README.md", "CHANGELOG.md", "COPYRIGHT"]
 
-[badges]
-travis-ci = { repository = "rust-random/rand" }
-appveyor = { repository = "rust-random/rand" }
-
 [features]
 # Meta-features:
 default = ["std", "std_rng"]
diff --git a/README.md b/README.md
index 6d1db896ddd..214d9ed41e0 100644
--- a/README.md
+++ b/README.md
@@ -1,7 +1,6 @@
 # Rand
 
-[![Build Status](https://travis-ci.org/rust-random/rand.svg?branch=master)](https://travis-ci.org/rust-random/rand)
-[![Build Status](https://ci.appveyor.com/api/projects/status/github/rust-random/rand?svg=true)](https://ci.appveyor.com/project/rust-random/rand)
+[![Test Status](https://github.com/rust-random/rand/workflows/Tests/badge.svg?event=push)](https://github.com/rust-random/rand/actions)
 [![Crate](https://img.shields.io/crates/v/rand.svg)](https://crates.io/crates/rand)
 [![Book](https://img.shields.io/badge/book-master-yellow.svg)](https://rust-random.github.io/book/)
 [![API](https://img.shields.io/badge/api-master-yellow.svg)](https://rust-random.github.io/rand)
@@ -104,8 +103,8 @@ greater, and 0.4 and 0.3 (since approx. June 2017) require Rustc version 1.15 or
 greater. Subsets of the Rand code may work with older Rust versions, but this is
 not supported.
 
-Travis CI always has a build with a pinned version of Rustc matching the oldest
-supported Rust release. The current policy is that this can be updated in any
+Continuous Integration (CI) will always test the minimum supported Rustc version
+(the MSRV). The current policy is that this can be updated in any
 Rand release if required, but the change must be noted in the changelog.
 
 ## Crate Features
diff --git a/appveyor.yml b/appveyor.yml
deleted file mode 100644
index c7d35ef2b33..00000000000
--- a/appveyor.yml
+++ /dev/null
@@ -1,48 +0,0 @@
-environment:
-
-  # At the time this was added AppVeyor was having troubles with checking
-  # revocation of SSL certificates of sites like static.rust-lang.org and what
-  # we think is crates.io. The libcurl HTTP client by default checks for
-  # revocation on Windows and according to a mailing list [1] this can be
-  # disabled.
-  #
-  # The `CARGO_HTTP_CHECK_REVOKE` env var here tells cargo to disable SSL
-  # revocation checking on Windows in libcurl. Note, though, that rustup, which
-  # we're using to download Rust here, also uses libcurl as the default backend.
-  # Unlike Cargo, however, rustup doesn't have a mechanism to disable revocation
-  # checking. To get rustup working we set `RUSTUP_USE_HYPER` which forces it to
-  # use the Hyper instead of libcurl backend. Both Hyper and libcurl use
-  # schannel on Windows but it appears that Hyper configures it slightly
-  # differently such that revocation checking isn't turned on by default.
-  #
-  # [1]: https://curl.haxx.se/mail/lib-2016-03/0202.html
-  RUSTUP_USE_HYPER: 1
-  CARGO_HTTP_CHECK_REVOKE: false
-
-  matrix:
-  - TARGET: x86_64-pc-windows-msvc
-  - TARGET: i686-pc-windows-msvc
-install:
-  - appveyor DownloadFile https://win.rustup.rs/ -FileName rustup-init.exe
-  - rustup-init.exe -y --default-host %TARGET% --default-toolchain nightly
-  - set PATH=%PATH%;C:\Users\appveyor\.cargo\bin
-  - rustc -V
-  - cargo -V
-
-build: false
-
-test_script:
-  - cargo test --tests --no-default-features
-  - cargo test --tests --no-default-features --features=alloc,getrandom
-  - cargo test --features simd_support
-  # all stable features:
-  - cargo test --features=serde1,log
-  - cargo test --benches --features=nightly
-  - cargo test --examples
-  - cargo test --manifest-path rand_core/Cargo.toml
-  - cargo test --manifest-path rand_core/Cargo.toml --no-default-features
-  - cargo test --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc
-  - cargo test --manifest-path rand_distr/Cargo.toml
-  - cargo test --manifest-path rand_pcg/Cargo.toml --features=serde1
-  - cargo test --manifest-path rand_chacha/Cargo.toml
-  - cargo test --manifest-path rand_hc/Cargo.toml
diff --git a/rand_chacha/Cargo.toml b/rand_chacha/Cargo.toml
index 2a17aa172bc..703cc86ac9b 100644
--- a/rand_chacha/Cargo.toml
+++ b/rand_chacha/Cargo.toml
@@ -14,10 +14,6 @@ keywords = ["random", "rng", "chacha"]
 categories = ["algorithms", "no-std"]
 edition = "2018"
 
-[badges]
-travis-ci = { repository = "rust-random/rand" }
-appveyor = { repository = "rust-random/rand" }
-
 [dependencies]
 rand_core = { path = "../rand_core", version = "0.5" }
 ppv-lite86 = { version = "0.2.8", default-features = false, features = ["simd"] }
diff --git a/rand_chacha/README.md b/rand_chacha/README.md
index b1928fd9cc8..edd754d791e 100644
--- a/rand_chacha/README.md
+++ b/rand_chacha/README.md
@@ -1,7 +1,6 @@
 # rand_chacha
 
-[![Build Status](https://travis-ci.org/rust-random/rand.svg)](https://travis-ci.org/rust-random/rand)
-[![Build Status](https://ci.appveyor.com/api/projects/status/github/rust-random/rand?svg=true)](https://ci.appveyor.com/project/rust-random/rand)
+[![Test Status](https://github.com/rust-random/rand/workflows/Tests/badge.svg?event=push)](https://github.com/rust-random/rand/actions)
 [![Latest version](https://img.shields.io/crates/v/rand_chacha.svg)](https://crates.io/crates/rand_chacha)
 [![Book](https://img.shields.io/badge/book-master-yellow.svg)](https://rust-random.github.io/book/)
 [![API](https://img.shields.io/badge/api-master-yellow.svg)](https://rust-random.github.io/rand/rand_chacha)
diff --git a/rand_core/Cargo.toml b/rand_core/Cargo.toml
index 4b85940ff70..831562689dc 100644
--- a/rand_core/Cargo.toml
+++ b/rand_core/Cargo.toml
@@ -14,10 +14,6 @@ keywords = ["random", "rng"]
 categories = ["algorithms", "no-std"]
 edition = "2018"
 
-[badges]
-travis-ci = { repository = "rust-random/rand" }
-appveyor = { repository = "rust-random/rand" }
-
 [features]
 std = ["alloc", "getrandom", "getrandom/std"]    # use std library; should be default but for above bug
 alloc = []  # enables Vec and Box support without std
diff --git a/rand_core/README.md b/rand_core/README.md
index 78c8083fc82..aaec728672c 100644
--- a/rand_core/README.md
+++ b/rand_core/README.md
@@ -1,7 +1,6 @@
 # rand_core
 
-[![Build Status](https://travis-ci.org/rust-random/rand.svg)](https://travis-ci.org/rust-random/rand)
-[![Build Status](https://ci.appveyor.com/api/projects/status/github/rust-random/rand?svg=true)](https://ci.appveyor.com/project/rust-random/rand)
+[![Test Status](https://github.com/rust-random/rand/workflows/Tests/badge.svg?event=push)](https://github.com/rust-random/rand/actions)
 [![Latest version](https://img.shields.io/crates/v/rand_core.svg)](https://crates.io/crates/rand_core)
 [![Book](https://img.shields.io/badge/book-master-yellow.svg)](https://rust-random.github.io/book/)
 [![API](https://img.shields.io/badge/api-master-yellow.svg)](https://rust-random.github.io/rand/rand_core)
diff --git a/rand_distr/Cargo.toml b/rand_distr/Cargo.toml
index fe40d179110..e6dc5462c24 100644
--- a/rand_distr/Cargo.toml
+++ b/rand_distr/Cargo.toml
@@ -15,10 +15,6 @@ categories = ["algorithms"]
 edition = "2018"
 include = ["src/", "LICENSE-*", "README.md", "CHANGELOG.md", "COPYRIGHT"]
 
-[badges]
-travis-ci = { repository = "rust-random/rand" }
-appveyor = { repository = "rust-random/rand" }
-
 [dependencies]
 rand = { path = "..", version = "0.7", default-features = false }
 num-traits = { version = "0.2", default-features = false, features = ["libm"] }
diff --git a/rand_distr/README.md b/rand_distr/README.md
index 9a67e5b3f93..29b5fe0853e 100644
--- a/rand_distr/README.md
+++ b/rand_distr/README.md
@@ -1,7 +1,6 @@
 # rand_distr
 
-[![Build Status](https://travis-ci.org/rust-random/rand.svg?branch=master)](https://travis-ci.org/rust-random/rand)
-[![Build Status](https://ci.appveyor.com/api/projects/status/github/rust-random/rand?svg=true)](https://ci.appveyor.com/project/rust-random/rand)
+[![Test Status](https://github.com/rust-random/rand/workflows/Tests/badge.svg?event=push)](https://github.com/rust-random/rand/actions)
 [![Latest version](https://img.shields.io/crates/v/rand_distr.svg)](https://crates.io/crates/rand_distr)
 [[![Book](https://img.shields.io/badge/book-master-yellow.svg)](https://rust-random.github.io/book/)
 [![API](https://img.shields.io/badge/api-master-yellow.svg)](https://rust-random.github.io/rand/rand_distr)
diff --git a/rand_distr/src/cauchy.rs b/rand_distr/src/cauchy.rs
index ffe86d00a9b..952b7f29dc9 100644
--- a/rand_distr/src/cauchy.rs
+++ b/rand_distr/src/cauchy.rs
@@ -159,8 +159,7 @@ mod test {
         gen_samples(10f32, 7.0, &mut buf);
         let expected = [15.023088, -5.446413, 3.7092876, 3.112482];
         for (a, b) in buf.iter().zip(expected.iter()) {
-            let (a, b) = (*a, *b);
-            assert!((a - b).abs() < 1e-6, "expected: {} = {}", a, b);
+            assert_almost_eq!(*a, *b, 1e-5);
         }
     }
 }
diff --git a/rand_distr/src/normal.rs b/rand_distr/src/normal.rs
index ae82799147a..8c3c8f8fd2f 100644
--- a/rand_distr/src/normal.rs
+++ b/rand_distr/src/normal.rs
@@ -345,7 +345,8 @@ mod tests {
         assert_almost_eq!(lnorm.norm.std_dev, 1.0, 2e-16);
 
         let lnorm = LogNormal::from_mean_cv(e.powf(1.5), (e - 1.0).sqrt()).unwrap();
-        assert_eq!((lnorm.norm.mean, lnorm.norm.std_dev), (1.0, 1.0));
+        assert_almost_eq!(lnorm.norm.mean, 1.0, 1e-15);
+        assert_eq!(lnorm.norm.std_dev, 1.0);
     }
     #[test]
     fn test_log_normal_invalid_sd() {
diff --git a/rand_distr/src/pareto.rs b/rand_distr/src/pareto.rs
index 217899ed9a7..3250c86ffe9 100644
--- a/rand_distr/src/pareto.rs
+++ b/rand_distr/src/pareto.rs
@@ -87,6 +87,7 @@ where F: Float, OpenClosed01: Distribution<F>
 #[cfg(test)]
 mod tests {
     use super::*;
+    use core::fmt::{Debug, Display, LowerExp};
 
     #[test]
     #[should_panic]
@@ -108,21 +109,20 @@ mod tests {
 
     #[test]
     fn value_stability() {
-        fn test_samples<F: Float + core::fmt::Debug, D: Distribution<F>>(
-            distr: D, zero: F, expected: &[F],
+        fn test_samples<F: Float + Debug + Display + LowerExp, D: Distribution<F>>(
+            distr: D, thresh: F, expected: &[F],
         ) {
             let mut rng = crate::test::rng(213);
-            let mut buf = [zero; 4];
-            for x in &mut buf {
-                *x = rng.sample(&distr);
+            for v in expected {
+                let x = rng.sample(&distr);
+                assert_almost_eq!(x, *v, thresh);
             }
-            assert_eq!(buf, expected);
         }
 
-        test_samples(Pareto::new(1.0, 1.0).unwrap(), 0f32, &[
+        test_samples(Pareto::new(1f32, 1.0).unwrap(), 1e-6, &[
             1.0423688, 2.1235929, 4.132709, 1.4679428,
         ]);
-        test_samples(Pareto::new(2.0, 0.5).unwrap(), 0f64, &[
+        test_samples(Pareto::new(2.0, 0.5).unwrap(), 1e-14, &[
             9.019295276219136,
             4.3097126018270595,
             6.837815045397157,
diff --git a/rand_distr/tests/value_stability.rs b/rand_distr/tests/value_stability.rs
index 986b9963283..65c49644a41 100644
--- a/rand_distr/tests/value_stability.rs
+++ b/rand_distr/tests/value_stability.rs
@@ -6,7 +6,8 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-use core::{fmt::Debug, cmp::PartialEq};
+use average::assert_almost_eq;
+use core::fmt::Debug;
 use rand::Rng;
 use rand_distr::*;
 
@@ -17,12 +18,48 @@ fn get_rng(seed: u64) -> impl rand::Rng {
     rand_pcg::Pcg32::new(seed, INC)
 }
 
-fn test_samples<F: Debug + Copy + PartialEq, D: Distribution<F>>(
+/// We only assert approximate equality since some platforms do not perform
+/// identically (i686-unknown-linux-gnu and most notably x86_64-pc-windows-gnu).
+trait ApproxEq {
+    fn assert_almost_eq(&self, rhs: &Self);
+}
+
+impl ApproxEq for f32 {
+    fn assert_almost_eq(&self, rhs: &Self) {
+        assert_almost_eq!(self, rhs, 1e-6);
+    }
+}
+impl ApproxEq for f64 {
+    fn assert_almost_eq(&self, rhs: &Self) {
+        assert_almost_eq!(self, rhs, 1e-14);
+    }
+}
+impl ApproxEq for u64 {
+    fn assert_almost_eq(&self, rhs: &Self) {
+        assert_eq!(self, rhs);
+    }
+}
+impl<T: ApproxEq> ApproxEq for [T; 2] {
+    fn assert_almost_eq(&self, rhs: &Self) {
+        self[0].assert_almost_eq(&rhs[0]);
+        self[1].assert_almost_eq(&rhs[1]);
+    }
+}
+impl<T: ApproxEq> ApproxEq for [T; 3] {
+    fn assert_almost_eq(&self, rhs: &Self) {
+        self[0].assert_almost_eq(&rhs[0]);
+        self[1].assert_almost_eq(&rhs[1]);
+        self[2].assert_almost_eq(&rhs[2]);
+    }
+}
+
+fn test_samples<F: Debug + ApproxEq, D: Distribution<F>>(
     seed: u64, distr: D, expected: &[F],
 ) {
     let mut rng = get_rng(seed);
-    for &val in expected {
-        assert_eq!(val, rng.sample(&distr));
+    for val in expected {
+        let x = rng.sample(&distr);
+        x.assert_almost_eq(val);
     }
 }
 
@@ -334,11 +371,12 @@ fn cauchy_stability() {
 
     // Unfortunately this test is not fully portable due to reliance on the
     // system's implementation of tanf (see doc on Cauchy struct).
+    // We use a lower threshold of 1e-5 here.
     let distr = Cauchy::new(10f32, 7.0).unwrap();
     let mut rng = get_rng(353);
     let expected = [15.023088, -5.446413, 3.7092876, 3.112482];
     for &a in expected.iter() {
         let b = rng.sample(&distr);
-        assert!((a - b).abs() < 1e-6, "expected: {} = {}", a, b);
+        assert_almost_eq!(a, b, 1e-5);
     }
 }
diff --git a/rand_hc/Cargo.toml b/rand_hc/Cargo.toml
index 84f53f80cdd..048f9aaa208 100644
--- a/rand_hc/Cargo.toml
+++ b/rand_hc/Cargo.toml
@@ -14,9 +14,5 @@ keywords = ["random", "rng", "hc128"]
 categories = ["algorithms", "no-std"]
 edition = "2018"
 
-[badges]
-travis-ci = { repository = "rust-random/rand" }
-appveyor = { repository = "rust-random/rand" }
-
 [dependencies]
 rand_core = { path = "../rand_core", version = "0.5" }
diff --git a/rand_hc/README.md b/rand_hc/README.md
index 4d992fec0c5..87f1c8915c1 100644
--- a/rand_hc/README.md
+++ b/rand_hc/README.md
@@ -1,7 +1,6 @@
 # rand_hc
 
-[![Build Status](https://travis-ci.org/rust-random/rand.svg)](https://travis-ci.org/rust-random/rand)
-[![Build Status](https://ci.appveyor.com/api/projects/status/github/rust-random/rand?svg=true)](https://ci.appveyor.com/project/rust-random/rand)
+[![Test Status](https://github.com/rust-random/rand/workflows/Tests/badge.svg?event=push)](https://github.com/rust-random/rand/actions)
 [![Latest version](https://img.shields.io/crates/v/rand_hc.svg)](https://crates.io/crates/rand_hc)
 [[![Book](https://img.shields.io/badge/book-master-yellow.svg)](https://rust-random.github.io/book/)
 [![API](https://img.shields.io/badge/api-master-yellow.svg)](https://rust-random.github.io/rand/rand_hc)
diff --git a/rand_pcg/Cargo.toml b/rand_pcg/Cargo.toml
index 9eb2eaf51e1..33e65c547dd 100644
--- a/rand_pcg/Cargo.toml
+++ b/rand_pcg/Cargo.toml
@@ -14,10 +14,6 @@ keywords = ["random", "rng", "pcg"]
 categories = ["algorithms", "no-std"]
 edition = "2018"
 
-[badges]
-travis-ci = { repository = "rust-random/rand" }
-appveyor = { repository = "rust-random/rand" }
-
 [features]
 serde1 = ["serde"]
 
diff --git a/rand_pcg/README.md b/rand_pcg/README.md
index 97204213c8d..736a789035c 100644
--- a/rand_pcg/README.md
+++ b/rand_pcg/README.md
@@ -1,7 +1,6 @@
 # rand_pcg
 
-[![Build Status](https://travis-ci.org/rust-random/rand.svg?branch=master)](https://travis-ci.org/rust-random/rand)
-[![Build Status](https://ci.appveyor.com/api/projects/status/github/rust-random/rand?svg=true)](https://ci.appveyor.com/project/rust-random/rand)
+[![Test Status](https://github.com/rust-random/rand/workflows/Tests/badge.svg?event=push)](https://github.com/rust-random/rand/actions)
 [![Latest version](https://img.shields.io/crates/v/rand_pcg.svg)](https://crates.io/crates/rand_pcg)
 [![Book](https://img.shields.io/badge/book-master-yellow.svg)](https://rust-random.github.io/book/)
 [![API](https://img.shields.io/badge/api-master-yellow.svg)](https://rust-random.github.io/rand/rand_pcg)
diff --git a/utils/ci/install.sh b/utils/ci/install.sh
deleted file mode 100644
index 8e636e18175..00000000000
--- a/utils/ci/install.sh
+++ /dev/null
@@ -1,49 +0,0 @@
-# From https://github.com/japaric/trust
-
-set -ex
-
-main() {
-    local target=
-    if [ $TRAVIS_OS_NAME = linux ]; then
-        target=x86_64-unknown-linux-musl
-        sort=sort
-    else
-        target=x86_64-apple-darwin
-        sort=gsort  # for `sort --sort-version`, from brew's coreutils.
-    fi
-
-    # Builds for iOS are done on OSX, but require the specific target to be
-    # installed.
-    case $TARGET in
-        aarch64-apple-ios)
-            rustup target install aarch64-apple-ios
-            ;;
-        armv7-apple-ios)
-            rustup target install armv7-apple-ios
-            ;;
-        armv7s-apple-ios)
-            rustup target install armv7s-apple-ios
-            ;;
-        i386-apple-ios)
-            rustup target install i386-apple-ios
-            ;;
-        x86_64-apple-ios)
-            rustup target install x86_64-apple-ios
-            ;;
-    esac
-
-    # This fetches latest stable release
-    local tag=$(git ls-remote --tags --refs --exit-code https://github.com/japaric/cross \
-                       | cut -d/ -f3 \
-                       | grep -E '^v[0.1.0-9.]+$' \
-                       | $sort --version-sort \
-                       | tail -n1)
-    curl -LSfs https://japaric.github.io/trust/install.sh | \
-        sh -s -- \
-           --force \
-           --git japaric/cross \
-           --tag $tag \
-           --target $target
-}
-
-main
diff --git a/utils/ci/install_cargo_web.sh b/utils/ci/install_cargo_web.sh
deleted file mode 100755
index b35f0691984..00000000000
--- a/utils/ci/install_cargo_web.sh
+++ /dev/null
@@ -1,15 +0,0 @@
-#!/bin/bash
-
-set -euo pipefail
-IFS=$'\n\t'
-
-CARGO_WEB_RELEASE=$(curl -L -s -H 'Accept: application/json' https://github.com/koute/cargo-web/releases/latest)
-CARGO_WEB_VERSION=$(echo $CARGO_WEB_RELEASE | sed -e 's/.*"tag_name":"\([^"]*\)".*/\1/')
-CARGO_WEB_URL="https://github.com/koute/cargo-web/releases/download/$CARGO_WEB_VERSION/cargo-web-x86_64-unknown-linux-gnu.gz"
-
-echo "Downloading cargo-web from: $CARGO_WEB_URL"
-curl -L $CARGO_WEB_URL | gzip -d > cargo-web
-chmod +x cargo-web
-
-mkdir -p ~/.cargo/bin
-mv cargo-web ~/.cargo/bin
diff --git a/utils/ci/miri.sh b/utils/ci/miri.sh
deleted file mode 100644
index 7e06091ff32..00000000000
--- a/utils/ci/miri.sh
+++ /dev/null
@@ -1,18 +0,0 @@
-set -ex
-
-MIRI_NIGHTLY=nightly-$(curl -s https://rust-lang.github.io/rustup-components-history/x86_64-unknown-linux-gnu/miri)
-echo "Installing latest nightly with Miri: $MIRI_NIGHTLY"
-rustup default "$MIRI_NIGHTLY"
-
-rustup component add miri
-cargo miri setup
-
-cargo miri test --no-default-features
-cargo miri test --features=log
-cargo miri test --manifest-path rand_core/Cargo.toml
-cargo miri test --manifest-path rand_core/Cargo.toml --features=serde1
-cargo miri test --manifest-path rand_core/Cargo.toml --no-default-features
-#cargo miri test --manifest-path rand_distr/Cargo.toml # no unsafe and lots of slow tests
-cargo miri test --manifest-path rand_pcg/Cargo.toml --features=serde1
-cargo miri test --manifest-path rand_chacha/Cargo.toml --no-default-features
-cargo miri test --manifest-path rand_hc/Cargo.toml
diff --git a/utils/ci/script.sh b/utils/ci/script.sh
deleted file mode 100644
index caef0767ca9..00000000000
--- a/utils/ci/script.sh
+++ /dev/null
@@ -1,59 +0,0 @@
-# Derived from https://github.com/japaric/trust
-
-set -ex
-
-# ----- Options -----
-
-# TARGET enables cross-building
-if [ -z $TARGET ]; then
-    CARGO=cargo
-elif [ "$TARGET" = "i686-unknown-linux-musl" ]; then
-    CARGO=cargo
-    TARGET="--target $TARGET"
-else
-    CARGO=cross
-    TARGET="--target $TARGET"
-fi
-
-# ALLOC defaults on; is disabled for rustc < 1.36
-if [ -z $ALLOC ]; then
-    ALLOC=1
-fi
-
-# NIGHTLY defaults off
-
-
-# ----- Script -----
-
-main() {
-  if [ "0$NIGHTLY" -ge 1 ]; then
-    $CARGO test $TARGET --all-features
-    $CARGO test $TARGET --benches --features=nightly
-    $CARGO test $TARGET --manifest-path rand_distr/Cargo.toml --benches
-  else
-    # all stable features:
-    $CARGO test $TARGET --features=serde1,log,small_rng
-  fi
-
-  if [ "$ALLOC" -ge 1 ]; then
-    $CARGO test $TARGET --tests --no-default-features --features=alloc,getrandom,small_rng
-    $CARGO test $TARGET --manifest-path rand_core/Cargo.toml --no-default-features --features=alloc
-  fi
-  
-  $CARGO test $TARGET --tests --no-default-features
-  $CARGO test $TARGET --examples
-  
-  $CARGO test $TARGET --manifest-path rand_core/Cargo.toml
-  $CARGO test $TARGET --manifest-path rand_core/Cargo.toml --no-default-features
-  $CARGO test $TARGET --manifest-path rand_core/Cargo.toml --no-default-features --features=getrandom
-  
-  $CARGO test $TARGET --manifest-path rand_distr/Cargo.toml
-  $CARGO test $TARGET --manifest-path rand_pcg/Cargo.toml --features=serde1
-  $CARGO test $TARGET --manifest-path rand_chacha/Cargo.toml
-  $CARGO test $TARGET --manifest-path rand_hc/Cargo.toml
-}
-
-# we don't run the "test phase" when doing deploys
-if [ -z $TRAVIS_TAG ]; then
-    main
-fi