diff --git a/.travis.yml b/.travis.yml
index ee744e1..2e54a81 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,6 +1,6 @@
 language: rust
 rust:
-  - 1.20.0
+  - 1.36.0
   - nightly
   - beta
   - stable
@@ -11,4 +11,5 @@ script: |
   ([ $TRAVIS_RUST_VERSION != nightly ] || cargo check --verbose --no-default-features) &&
   ([ $TRAVIS_RUST_VERSION != nightly ] || cargo test --verbose --features union) &&
   ([ $TRAVIS_RUST_VERSION != nightly ] || cargo test --verbose --all-features) &&
-  ([ $TRAVIS_RUST_VERSION != nightly ] || cargo bench --verbose bench)
+  ([ $TRAVIS_RUST_VERSION != nightly ] || cargo bench --verbose bench) &&
+  ([ $TRAVIS_RUST_VERSION != nightly ] || bash ./scripts/run_miri.sh)
diff --git a/scripts/run_miri.sh b/scripts/run_miri.sh
new file mode 100644
index 0000000..42f2884
--- /dev/null
+++ b/scripts/run_miri.sh
@@ -0,0 +1,21 @@
+#!/usr/bin/bash
+
+set -ex
+
+# Clean out our target dir, which may have artifacts compiled by a version of
+# rust different from the one we're about to download.
+cargo clean
+
+# Install and run the latest version of nightly where miri built successfully.
+# Taken from: https://github.com/rust-lang/miri#running-miri-on-ci
+
+MIRI_NIGHTLY=nightly-$(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 --verbose -- -- -Zunstable-options --exclude-should-panic
+cargo miri test --verbose --features union -- -- -Zunstable-options --exclude-should-panic
+cargo miri test --verbose --all-features -- -- -Zunstable-options --exclude-should-panic