diff --git a/library/core/src/option.rs b/library/core/src/option.rs
index 8057ff0759107..d4e9c384f9302 100644
--- a/library/core/src/option.rs
+++ b/library/core/src/option.rs
@@ -285,6 +285,19 @@
 //! assert_eq!(res, ["error!", "error!", "foo", "error!", "bar"]);
 //! ```
 //!
+//! ## Comparison operators
+//!
+//! If `T` implements [`PartialOrd`] then [`Option<T>`] will derive its
+//! [`PartialOrd`] implementation.  With this order, [`None`] compares as
+//! less than any [`Some`], and two [`Some`] compare the same way as their
+//! contained values would in `T`.  If `T` also implements
+//! [`Ord`], then so does [`Option<T>`].
+//!
+//! ```
+//! assert!(None < Some(0));
+//! assert!(Some(0) < Some(1));
+//! ```
+//!
 //! ## Iterating over `Option`
 //!
 //! An [`Option`] can be iterated over. This can be helpful if you need an
diff --git a/library/core/src/result.rs b/library/core/src/result.rs
index 53aaa5219b1d4..861790e8a4099 100644
--- a/library/core/src/result.rs
+++ b/library/core/src/result.rs
@@ -379,6 +379,24 @@
 //! [`and_then`]: Result::and_then
 //! [`or_else`]: Result::or_else
 //!
+//! ## Comparison operators
+//!
+//! If `T` and `E` both implement [`PartialOrd`] then [`Result<T, E>`] will
+//! derive its [`PartialOrd`] implementation.  With this order, an [`Ok`]
+//! compares as less than any [`Err`], while two [`Ok`] or two [`Err`]
+//! compare as their contained values would in `T` or `E` respectively.  If `T`
+//! and `E` both also implement [`Ord`], then so does [`Result<T, E>`].
+//!
+//! ```
+//! assert!(Ok(1) < Err(0));
+//! let x: Result<i32, ()> = Ok(0);
+//! let y = Ok(1);
+//! assert!(x < y);
+//! let x: Result<(), i32> = Err(0);
+//! let y = Err(1);
+//! assert!(x < y);
+//! ```
+//!
 //! ## Iterating over `Result`
 //!
 //! A [`Result`] can be iterated over. This can be helpful if you need an