diff --git a/tokio/src/io/poll_evented.rs b/tokio/src/io/poll_evented.rs
index 785968f43f8..9054c3b8733 100644
--- a/tokio/src/io/poll_evented.rs
+++ b/tokio/src/io/poll_evented.rs
@@ -173,7 +173,7 @@ where
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn new(io: E) -> io::Result<Self> {
         PollEvented::new_with_ready(io, mio::Ready::all())
     }
@@ -201,7 +201,7 @@ where
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn new_with_ready(io: E, ready: mio::Ready) -> io::Result<Self> {
         let registration = Registration::new_with_ready(&io, ready)?;
         Ok(Self {
diff --git a/tokio/src/io/registration.rs b/tokio/src/io/registration.rs
index 63aaff56d86..8206507280d 100644
--- a/tokio/src/io/registration.rs
+++ b/tokio/src/io/registration.rs
@@ -67,7 +67,7 @@ impl Registration {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn new<T>(io: &T) -> io::Result<Registration>
     where
         T: Evented,
@@ -104,7 +104,7 @@ impl Registration {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn new_with_ready<T>(io: &T, ready: mio::Ready) -> io::Result<Registration>
     where
         T: Evented,
diff --git a/tokio/src/net/tcp/listener.rs b/tokio/src/net/tcp/listener.rs
index fd79b259b92..44945e387b4 100644
--- a/tokio/src/net/tcp/listener.rs
+++ b/tokio/src/net/tcp/listener.rs
@@ -262,7 +262,7 @@ impl TcpListener {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn from_std(listener: net::TcpListener) -> io::Result<TcpListener> {
         let io = mio::net::TcpListener::from_std(listener)?;
         let io = PollEvented::new(io)?;
diff --git a/tokio/src/net/tcp/stream.rs b/tokio/src/net/tcp/stream.rs
index e624fb9d954..e0348724cff 100644
--- a/tokio/src/net/tcp/stream.rs
+++ b/tokio/src/net/tcp/stream.rs
@@ -187,7 +187,7 @@ impl TcpStream {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn from_std(stream: net::TcpStream) -> io::Result<TcpStream> {
         let io = mio::net::TcpStream::from_stream(stream)?;
         let io = PollEvented::new(io)?;
diff --git a/tokio/src/net/udp/socket.rs b/tokio/src/net/udp/socket.rs
index 16e537739d4..f9d88372035 100644
--- a/tokio/src/net/udp/socket.rs
+++ b/tokio/src/net/udp/socket.rs
@@ -64,7 +64,7 @@ impl UdpSocket {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn from_std(socket: net::UdpSocket) -> io::Result<UdpSocket> {
         let io = mio::net::UdpSocket::from_socket(socket)?;
         let io = PollEvented::new(io)?;
diff --git a/tokio/src/net/unix/datagram/socket.rs b/tokio/src/net/unix/datagram/socket.rs
index 2282f96a3f6..ba3a10c4882 100644
--- a/tokio/src/net/unix/datagram/socket.rs
+++ b/tokio/src/net/unix/datagram/socket.rs
@@ -164,7 +164,7 @@ impl UnixDatagram {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a Tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     /// # Examples
     /// ```
     /// # use std::error::Error;
diff --git a/tokio/src/net/unix/listener.rs b/tokio/src/net/unix/listener.rs
index 9b76cb01fd7..119dc6fb41c 100644
--- a/tokio/src/net/unix/listener.rs
+++ b/tokio/src/net/unix/listener.rs
@@ -60,7 +60,7 @@ impl UnixListener {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn bind<P>(path: P) -> io::Result<UnixListener>
     where
         P: AsRef<Path>,
@@ -82,7 +82,7 @@ impl UnixListener {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn from_std(listener: net::UnixListener) -> io::Result<UnixListener> {
         let listener = mio_uds::UnixListener::from_listener(listener)?;
         let io = PollEvented::new(listener)?;
diff --git a/tokio/src/net/unix/stream.rs b/tokio/src/net/unix/stream.rs
index 559fe02a625..6f49849aef3 100644
--- a/tokio/src/net/unix/stream.rs
+++ b/tokio/src/net/unix/stream.rs
@@ -54,7 +54,7 @@ impl UnixStream {
     ///
     /// The runtime is usually set implicitly when this function is called
     /// from a future driven by a tokio runtime, otherwise runtime can be set
-    /// explicitly with [`Handle::enter`](crate::runtime::Handle::enter) function.
+    /// explicitly with [`Runtime::enter`](crate::runtime::Runtime::enter) function.
     pub fn from_std(stream: net::UnixStream) -> io::Result<UnixStream> {
         let stream = mio_uds::UnixStream::from_stream(stream)?;
         let io = PollEvented::new(stream)?;
diff --git a/tokio/src/runtime/blocking/pool.rs b/tokio/src/runtime/blocking/pool.rs
index 5ad5f5f8421..47895fcf477 100644
--- a/tokio/src/runtime/blocking/pool.rs
+++ b/tokio/src/runtime/blocking/pool.rs
@@ -6,6 +6,7 @@ use crate::runtime::blocking::schedule::NoopSchedule;
 use crate::runtime::blocking::shutdown;
 use crate::runtime::blocking::task::BlockingTask;
 use crate::runtime::builder::ThreadNameFn;
+use crate::runtime::context;
 use crate::runtime::task::{self, JoinHandle};
 use crate::runtime::{Builder, Callback, Handle};
 
@@ -67,7 +68,7 @@ pub(crate) fn spawn_blocking<F, R>(func: F) -> JoinHandle<R>
 where
     F: FnOnce() -> R + Send + 'static,
 {
-    let rt = Handle::current();
+    let rt = context::current().expect("not currently running on the Tokio runtime.");
 
     let (task, handle) = task::joinable(BlockingTask::new(func));
     let _ = rt.blocking_spawner.spawn(task, &rt);
@@ -79,7 +80,7 @@ pub(crate) fn try_spawn_blocking<F, R>(func: F) -> Result<(), ()>
 where
     F: FnOnce() -> R + Send + 'static,
 {
-    let rt = Handle::current();
+    let rt = context::current().expect("not currently running on the Tokio runtime.");
 
     let (task, _handle) = task::joinable(BlockingTask::new(func));
     rt.blocking_spawner.spawn(task, &rt)
diff --git a/tokio/src/runtime/builder.rs b/tokio/src/runtime/builder.rs
index d6e2fe2f0af..1b52a14970e 100644
--- a/tokio/src/runtime/builder.rs
+++ b/tokio/src/runtime/builder.rs
@@ -67,7 +67,7 @@ pub struct Builder {
     pub(super) before_stop: Option<Callback>,
 }
 
-pub(crate) type ThreadNameFn = Arc<dyn Fn() -> String + Send + Sync + 'static>;
+pub(crate) type ThreadNameFn = std::sync::Arc<dyn Fn() -> String + Send + Sync + 'static>;
 
 #[derive(Debug, Clone, Copy)]
 enum Kind {
@@ -100,7 +100,7 @@ impl Builder {
             max_threads: 512,
 
             // Default thread name
-            thread_name: Arc::new(|| "tokio-runtime-worker".into()),
+            thread_name: std::sync::Arc::new(|| "tokio-runtime-worker".into()),
 
             // Do not set a stack size by default
             thread_stack_size: None,
@@ -212,7 +212,7 @@ impl Builder {
     /// ```
     pub fn thread_name(&mut self, val: impl Into<String>) -> &mut Self {
         let val = val.into();
-        self.thread_name = Arc::new(move || val.clone());
+        self.thread_name = std::sync::Arc::new(move || val.clone());
         self
     }
 
@@ -240,7 +240,7 @@ impl Builder {
     where
         F: Fn() -> String + Send + Sync + 'static,
     {
-        self.thread_name = Arc::new(f);
+        self.thread_name = std::sync::Arc::new(f);
         self
     }
 
diff --git a/tokio/src/runtime/context.rs b/tokio/src/runtime/context.rs
index 1b267f481e2..c42b3432dea 100644
--- a/tokio/src/runtime/context.rs
+++ b/tokio/src/runtime/context.rs
@@ -7,8 +7,10 @@ thread_local! {
     static CONTEXT: RefCell<Option<Handle>> = RefCell::new(None)
 }
 
-pub(crate) fn current() -> Option<Handle> {
-    CONTEXT.with(|ctx| ctx.borrow().clone())
+cfg_blocking_impl! {
+    pub(crate) fn current() -> Option<Handle> {
+        CONTEXT.with(|ctx| ctx.borrow().clone())
+    }
 }
 
 cfg_io_driver! {
diff --git a/tokio/src/runtime/handle.rs b/tokio/src/runtime/handle.rs
index 837fd72edc1..516ad4b3aad 100644
--- a/tokio/src/runtime/handle.rs
+++ b/tokio/src/runtime/handle.rs
@@ -33,15 +33,4 @@ impl Handle {
     {
         context::enter(self.clone(), f)
     }
-
-    /// Returns a `Handle` view over the currently running `Runtime`
-    ///
-    /// # Panic
-    ///
-    /// This will panic if called outside the context of a Tokio runtime. That means that you must
-    /// call this on one of the threads **being run by the runtime**. Calling this from within a
-    /// thread created by `std::thread::spawn` (for example) will cause a panic.
-    pub(crate) fn current() -> Self {
-        context::current().expect("not currently running on the Tokio runtime.")
-    }
 }
diff --git a/tokio/src/runtime/mod.rs b/tokio/src/runtime/mod.rs
index 7d4e41b8665..9d430cfaf43 100644
--- a/tokio/src/runtime/mod.rs
+++ b/tokio/src/runtime/mod.rs
@@ -409,10 +409,10 @@ impl Runtime {
     /// complete, and yielding its resolved result. Any tasks or timers which
     /// the future spawns internally will be executed on the runtime.
     ///
-    /// `&mut` is required as calling `block_on` **may** result in advancing the
-    /// state of the runtime. The details depend on how the runtime is
-    /// configured. [`runtime::Handle::block_on`][handle] provides a version
-    /// that takes `&self`.
+    /// When this runtime is configured with `core_threads = 0` only the first call
+    /// to `block_on` will run the io/timer driver. All other calls _before_ the first
+    /// `block_on` completes will just hook into that driver. This means the driver
+    /// may be passed around from thread to thread manually by the user.
     ///
     /// This method may not be called from an asynchronous context.
     ///
@@ -477,11 +477,8 @@ impl Runtime {
     /// have an executor available on creation such as [`Delay`] or [`TcpStream`].
     /// It will also allow you to call methods such as [`tokio::spawn`].
     ///
-    /// This function is also available as [`Handle::enter`].
-    ///
     /// [`Delay`]: struct@crate::time::Delay
     /// [`TcpStream`]: struct@crate::net::TcpStream
-    /// [`Handle::enter`]: fn@crate::runtime::Handle::enter
     /// [`tokio::spawn`]: fn@crate::spawn
     ///
     /// # Example
diff --git a/tokio/src/task/spawn.rs b/tokio/src/task/spawn.rs
index d6e771184f2..280e90ead04 100644
--- a/tokio/src/task/spawn.rs
+++ b/tokio/src/task/spawn.rs
@@ -18,7 +18,7 @@ doc_rt_core! {
     ///
     /// This function must be called from the context of a Tokio runtime. Tasks running on
     /// the Tokio runtime are always inside its context, but you can also enter the context
-    /// using the [`Handle::enter`](crate::runtime::Handle::enter()) method.
+    /// using the [`Runtime::enter`](crate::runtime::Runtime::enter()) method.
     ///
     /// # Examples
     ///