diff --git a/src/doc/src/guide/dependencies.md b/src/doc/src/guide/dependencies.md
index a47f747e4d6..94419f15b7a 100644
--- a/src/doc/src/guide/dependencies.md
+++ b/src/doc/src/guide/dependencies.md
@@ -20,11 +20,11 @@ use. This example adds a dependency of the `time` crate:
 time = "0.1.12"
 ```
 
-The version string is a [semver] version requirement. The [specifying
+The version string is a [SemVer] version requirement. The [specifying
 dependencies](../reference/specifying-dependencies.md) docs have more information about
 the options you have here.
 
-[semver]: https://github.com/steveklabnik/semver#requirements
+[SemVer]: https://semver.org
 
 If we also wanted to add a dependency on the `regex` crate, we would not need
 to add `[dependencies]` for each crate listed. Here's what your whole
diff --git a/src/doc/src/reference/registries.md b/src/doc/src/reference/registries.md
index 96eb15e082c..ef23caeee1f 100644
--- a/src/doc/src/reference/registries.md
+++ b/src/doc/src/reference/registries.md
@@ -222,9 +222,9 @@ explaining the format of the entry.
             // this is the new name. The original package name is stored in
             // the `package` field.
             "name": "rand",
-            // The semver requirement for this dependency.
+            // The SemVer requirement for this dependency.
             // This must be a valid version requirement defined at
-            // https://github.com/steveklabnik/semver#requirements.
+            // https://doc.rust-lang.org/cargo/reference/specifying-dependencies.html.
             "req": "^0.6",
             // Array of features (as strings) enabled for this dependency.
             "features": ["i128_support"],
diff --git a/src/doc/src/reference/specifying-dependencies.md b/src/doc/src/reference/specifying-dependencies.md
index d60d523bd92..bfdadc7efc8 100644
--- a/src/doc/src/reference/specifying-dependencies.md
+++ b/src/doc/src/reference/specifying-dependencies.md
@@ -19,35 +19,30 @@ guide](../guide/index.md), we specified a dependency on the `time` crate:
 time = "0.1.12"
 ```
 
-The string `"0.1.12"` is a [semver] version requirement. Since this
-string does not have any operators in it, it is interpreted the same way as
-if we had specified `"^0.1.12"`, which is called a caret requirement.
-
-[semver]: https://github.com/steveklabnik/semver#requirements
-
-### Caret requirements
-
-**Caret requirements** allow SemVer compatible updates to a specified version.
-An update is allowed if the new version number does not modify the left-most
-non-zero digit in the major, minor, patch grouping. In this case, if we ran
-`cargo update -p time`, cargo should update us to version `0.1.13` if it is the
-latest `0.1.z` release, but would not update us to `0.2.0`. If instead we had
-specified the version string as `^1.0`, cargo should update to `1.1` if it is
-the latest `1.y` release, but not `2.0`. The version `0.0.x` is not considered
-compatible with any other version.
-
-Here are some more examples of caret requirements and the versions that would
+The string `"0.1.12"` is a version requirement. Although it looks like a
+specific *version* of the `time` crate, it actually specifies a *range* of
+versions and allows [SemVer] compatible updates. An update is allowed if the new
+version number does not modify the left-most non-zero digit in the major, minor,
+patch grouping. In this case, if we ran `cargo update -p time`, cargo should
+update us to version `0.1.13` if it is the latest `0.1.z` release, but would not
+update us to `0.2.0`. If instead we had specified the version string as `1.0`,
+cargo should update to `1.1` if it is the latest `1.y` release, but not `2.0`.
+The version `0.0.x` is not considered compatible with any other version.
+
+[SemVer]: https://semver.org
+
+Here are some more examples of version requirements and the versions that would
 be allowed with them:
 
 ```notrust
-^1.2.3  :=  >=1.2.3, <2.0.0
-^1.2    :=  >=1.2.0, <2.0.0
-^1      :=  >=1.0.0, <2.0.0
-^0.2.3  :=  >=0.2.3, <0.3.0
-^0.2    :=  >=0.2.0, <0.3.0
-^0.0.3  :=  >=0.0.3, <0.0.4
-^0.0    :=  >=0.0.0, <0.1.0
-^0      :=  >=0.0.0, <1.0.0
+1.2.3  :=  >=1.2.3, <2.0.0
+1.2    :=  >=1.2.0, <2.0.0
+1      :=  >=1.0.0, <2.0.0
+0.2.3  :=  >=0.2.3, <0.3.0
+0.2    :=  >=0.2.0, <0.3.0
+0.0.3  :=  >=0.0.3, <0.0.4
+0.0    :=  >=0.0.0, <0.1.0
+0      :=  >=0.0.0, <1.0.0
 ```
 
 This compatibility convention is different from SemVer in the way it treats
@@ -55,6 +50,14 @@ versions before 1.0.0. While SemVer says there is no compatibility before
 1.0.0, Cargo considers `0.x.y` to be compatible with `0.x.z`, where `y ≥ z`
 and `x > 0`.
 
+It is possible to further tweak the logic for selecting compatible versions
+using special operators, though it shouldn't be necessary most of the time.
+
+### Caret requirements
+
+**Caret requirements** are an alternative syntax for the default strategy,
+`^1.2.3` is exactly equivalent to `1.2.3`.
+
 ### Tilde requirements
 
 **Tilde requirements** specify a minimal version with some ability to update.