diff --git a/src/regex/bytes.rs b/src/regex/bytes.rs
index ea4f7cd65..7b7aad574 100644
--- a/src/regex/bytes.rs
+++ b/src/regex/bytes.rs
@@ -651,6 +651,9 @@ impl Regex {
     /// case, this implementation will likely return a `Cow::Borrowed` value
     /// such that no allocation is performed.
     ///
+    /// When a `Cow::Borrowed` is returned, the value returned is guaranteed
+    /// to be equivalent to the `haystack` given.
+    ///
     /// # Replacement string syntax
     ///
     /// All instances of `$ref` in the replacement string are replaced with
@@ -761,6 +764,13 @@ impl Regex {
     /// replacement provided. This is the same as calling `replacen` with
     /// `limit` set to `0`.
     ///
+    /// If no match is found, then the haystack is returned unchanged. In that
+    /// case, this implementation will likely return a `Cow::Borrowed` value
+    /// such that no allocation is performed.
+    ///
+    /// When a `Cow::Borrowed` is returned, the value returned is guaranteed
+    /// to be equivalent to the `haystack` given.
+    ///
     /// The documentation for [`Regex::replace`] goes into more detail about
     /// what kinds of replacement strings are supported.
     ///
@@ -855,6 +865,13 @@ impl Regex {
     /// matches are replaced. That is, `Regex::replace_all(hay, rep)` is
     /// equivalent to `Regex::replacen(hay, 0, rep)`.
     ///
+    /// If no match is found, then the haystack is returned unchanged. In that
+    /// case, this implementation will likely return a `Cow::Borrowed` value
+    /// such that no allocation is performed.
+    ///
+    /// When a `Cow::Borrowed` is returned, the value returned is guaranteed
+    /// to be equivalent to the `haystack` given.
+    ///
     /// The documentation for [`Regex::replace`] goes into more detail about
     /// what kinds of replacement strings are supported.
     ///
diff --git a/src/regex/string.rs b/src/regex/string.rs
index 824f45c69..dba94d46e 100644
--- a/src/regex/string.rs
+++ b/src/regex/string.rs
@@ -642,6 +642,9 @@ impl Regex {
     /// case, this implementation will likely return a `Cow::Borrowed` value
     /// such that no allocation is performed.
     ///
+    /// When a `Cow::Borrowed` is returned, the value returned is guaranteed
+    /// to be equivalent to the `haystack` given.
+    ///
     /// # Replacement string syntax
     ///
     /// All instances of `$ref` in the replacement string are replaced with
@@ -748,6 +751,13 @@ impl Regex {
     /// replacement provided. This is the same as calling `replacen` with
     /// `limit` set to `0`.
     ///
+    /// If no match is found, then the haystack is returned unchanged. In that
+    /// case, this implementation will likely return a `Cow::Borrowed` value
+    /// such that no allocation is performed.
+    ///
+    /// When a `Cow::Borrowed` is returned, the value returned is guaranteed
+    /// to be equivalent to the `haystack` given.
+    ///
     /// The documentation for [`Regex::replace`] goes into more detail about
     /// what kinds of replacement strings are supported.
     ///
@@ -842,6 +852,13 @@ impl Regex {
     /// matches are replaced. That is, `Regex::replace_all(hay, rep)` is
     /// equivalent to `Regex::replacen(hay, 0, rep)`.
     ///
+    /// If no match is found, then the haystack is returned unchanged. In that
+    /// case, this implementation will likely return a `Cow::Borrowed` value
+    /// such that no allocation is performed.
+    ///
+    /// When a `Cow::Borrowed` is returned, the value returned is guaranteed
+    /// to be equivalent to the `haystack` given.
+    ///
     /// The documentation for [`Regex::replace`] goes into more detail about
     /// what kinds of replacement strings are supported.
     ///