diff --git a/src/map.rs b/src/map.rs
index 2cce45fd..339bcd0e 100644
--- a/src/map.rs
+++ b/src/map.rs
@@ -1303,6 +1303,34 @@ impl<K, V, S> IndexMap<K, V, S> {
         self.as_slice().binary_search_by_key(b, f)
     }
 
+    /// Checks if the keys of this map are sorted.
+    #[inline]
+    pub fn is_sorted(&self) -> bool
+    where
+        K: PartialOrd,
+    {
+        self.as_slice().is_sorted()
+    }
+
+    /// Checks if this map is sorted using the given comparator function.
+    #[inline]
+    pub fn is_sorted_by<'a, F>(&'a self, cmp: F) -> bool
+    where
+        F: FnMut(&'a K, &'a V, &'a K, &'a V) -> bool,
+    {
+        self.as_slice().is_sorted_by(cmp)
+    }
+
+    /// Checks if this map is sorted using the given sort-key function.
+    #[inline]
+    pub fn is_sorted_by_key<'a, F, T>(&'a self, sort_key: F) -> bool
+    where
+        F: FnMut(&'a K, &'a V) -> T,
+        T: PartialOrd,
+    {
+        self.as_slice().is_sorted_by_key(sort_key)
+    }
+
     /// Returns the index of the partition point of a sorted map according to the given predicate
     /// (the index of the first element of the second partition).
     ///
diff --git a/src/map/slice.rs b/src/map/slice.rs
index b0537a30..59e685e3 100644
--- a/src/map/slice.rs
+++ b/src/map/slice.rs
@@ -258,6 +258,55 @@ impl<K, V> Slice<K, V> {
         self.binary_search_by(|k, v| f(k, v).cmp(b))
     }
 
+    /// Checks if the keys of this slice are sorted.
+    #[inline]
+    pub fn is_sorted(&self) -> bool
+    where
+        K: PartialOrd,
+    {
+        // TODO(MSRV 1.82): self.entries.is_sorted_by(|a, b| a.key <= b.key)
+        self.is_sorted_by_key(|k, _| k)
+    }
+
+    /// Checks if this slice is sorted using the given comparator function.
+    #[inline]
+    pub fn is_sorted_by<'a, F>(&'a self, mut cmp: F) -> bool
+    where
+        F: FnMut(&'a K, &'a V, &'a K, &'a V) -> bool,
+    {
+        // TODO(MSRV 1.82): self.entries
+        //     .is_sorted_by(move |a, b| cmp(&a.key, &a.value, &b.key, &b.value))
+        let mut iter = self.entries.iter();
+        match iter.next() {
+            Some(mut prev) => iter.all(move |next| {
+                let sorted = cmp(&prev.key, &prev.value, &next.key, &next.value);
+                prev = next;
+                sorted
+            }),
+            None => true,
+        }
+    }
+
+    /// Checks if this slice is sorted using the given sort-key function.
+    #[inline]
+    pub fn is_sorted_by_key<'a, F, T>(&'a self, mut sort_key: F) -> bool
+    where
+        F: FnMut(&'a K, &'a V) -> T,
+        T: PartialOrd,
+    {
+        // TODO(MSRV 1.82): self.entries
+        //     .is_sorted_by_key(move |a| sort_key(&a.key, &a.value))
+        let mut iter = self.entries.iter().map(move |a| sort_key(&a.key, &a.value));
+        match iter.next() {
+            Some(mut prev) => iter.all(move |next| {
+                let sorted = prev <= next;
+                prev = next;
+                sorted
+            }),
+            None => true,
+        }
+    }
+
     /// Returns the index of the partition point of a sorted map according to the given predicate
     /// (the index of the first element of the second partition).
     ///
diff --git a/src/map/tests.rs b/src/map/tests.rs
index 08692866..79041905 100644
--- a/src/map/tests.rs
+++ b/src/map/tests.rs
@@ -1264,3 +1264,49 @@ fn insert_sorted_by() {
     }
     assert_eq!(values, *map.as_slice());
 }
+
+#[test]
+fn is_sorted() {
+    fn expect(map: &IndexMap<i32, i32>, e: [bool; 7]) {
+        assert_eq!(e[0], map.is_sorted());
+        assert_eq!(e[1], map.is_sorted_by(|k1, _, k2, _| k1 < k2));
+        assert_eq!(e[2], map.is_sorted_by(|k1, _, k2, _| k1 > k2));
+        assert_eq!(e[3], map.is_sorted_by(|_, v1, _, v2| v1 < v2));
+        assert_eq!(e[4], map.is_sorted_by(|_, v1, _, v2| v1 > v2));
+        assert_eq!(e[5], map.is_sorted_by_key(|k, _| k));
+        assert_eq!(e[6], map.is_sorted_by_key(|_, v| v));
+    }
+
+    let mut map = IndexMap::from_iter((0..10).map(|i| (i, i * i)));
+    expect(&map, [true, true, false, true, false, true, true]);
+
+    map[5] = -1;
+    expect(&map, [true, true, false, false, false, true, false]);
+
+    map[5] = 25;
+    map.replace_index(5, -1).unwrap();
+    expect(&map, [false, false, false, true, false, false, true]);
+}
+
+#[test]
+fn is_sorted_trivial() {
+    fn expect(map: &IndexMap<i32, i32>, e: [bool; 5]) {
+        assert_eq!(e[0], map.is_sorted());
+        assert_eq!(e[1], map.is_sorted_by(|_, _, _, _| true));
+        assert_eq!(e[2], map.is_sorted_by(|_, _, _, _| false));
+        assert_eq!(e[3], map.is_sorted_by_key(|_, _| 0f64));
+        assert_eq!(e[4], map.is_sorted_by_key(|_, _| f64::NAN));
+    }
+
+    let mut map = IndexMap::new();
+    expect(&map, [true, true, true, true, true]);
+
+    map.insert(0, 0);
+    expect(&map, [true, true, true, true, true]);
+
+    map.insert(1, 1);
+    expect(&map, [true, true, false, true, false]);
+
+    map.reverse();
+    expect(&map, [false, true, false, true, false]);
+}
diff --git a/src/set.rs b/src/set.rs
index 9a527f8d..df686a65 100644
--- a/src/set.rs
+++ b/src/set.rs
@@ -1074,6 +1074,34 @@ impl<T, S> IndexSet<T, S> {
         self.as_slice().binary_search_by_key(b, f)
     }
 
+    /// Checks if the values of this set are sorted.
+    #[inline]
+    pub fn is_sorted(&self) -> bool
+    where
+        T: PartialOrd,
+    {
+        self.as_slice().is_sorted()
+    }
+
+    /// Checks if this set is sorted using the given comparator function.
+    #[inline]
+    pub fn is_sorted_by<'a, F>(&'a self, cmp: F) -> bool
+    where
+        F: FnMut(&'a T, &'a T) -> bool,
+    {
+        self.as_slice().is_sorted_by(cmp)
+    }
+
+    /// Checks if this set is sorted using the given sort-key function.
+    #[inline]
+    pub fn is_sorted_by_key<'a, F, K>(&'a self, sort_key: F) -> bool
+    where
+        F: FnMut(&'a T) -> K,
+        K: PartialOrd,
+    {
+        self.as_slice().is_sorted_by_key(sort_key)
+    }
+
     /// Returns the index of the partition point of a sorted set according to the given predicate
     /// (the index of the first element of the second partition).
     ///
diff --git a/src/set/slice.rs b/src/set/slice.rs
index ee79c8eb..666459db 100644
--- a/src/set/slice.rs
+++ b/src/set/slice.rs
@@ -160,6 +160,53 @@ impl<T> Slice<T> {
         self.binary_search_by(|k| f(k).cmp(b))
     }
 
+    /// Checks if the values of this slice are sorted.
+    #[inline]
+    pub fn is_sorted(&self) -> bool
+    where
+        T: PartialOrd,
+    {
+        // TODO(MSRV 1.82): self.entries.is_sorted_by(|a, b| a.key <= b.key)
+        self.is_sorted_by(T::le)
+    }
+
+    /// Checks if this slice is sorted using the given comparator function.
+    #[inline]
+    pub fn is_sorted_by<'a, F>(&'a self, mut cmp: F) -> bool
+    where
+        F: FnMut(&'a T, &'a T) -> bool,
+    {
+        // TODO(MSRV 1.82): self.entries.is_sorted_by(move |a, b| cmp(&a.key, &b.key))
+        let mut iter = self.entries.iter();
+        match iter.next() {
+            Some(mut prev) => iter.all(move |next| {
+                let sorted = cmp(&prev.key, &next.key);
+                prev = next;
+                sorted
+            }),
+            None => true,
+        }
+    }
+
+    /// Checks if this slice is sorted using the given sort-key function.
+    #[inline]
+    pub fn is_sorted_by_key<'a, F, K>(&'a self, mut sort_key: F) -> bool
+    where
+        F: FnMut(&'a T) -> K,
+        K: PartialOrd,
+    {
+        // TODO(MSRV 1.82): self.entries.is_sorted_by_key(move |a| sort_key(&a.key))
+        let mut iter = self.entries.iter().map(move |a| sort_key(&a.key));
+        match iter.next() {
+            Some(mut prev) => iter.all(move |next| {
+                let sorted = prev <= next;
+                prev = next;
+                sorted
+            }),
+            None => true,
+        }
+    }
+
     /// Returns the index of the partition point of a sorted set according to the given predicate
     /// (the index of the first element of the second partition).
     ///
diff --git a/src/set/tests.rs b/src/set/tests.rs
index e59f514c..bf761e08 100644
--- a/src/set/tests.rs
+++ b/src/set/tests.rs
@@ -1019,3 +1019,42 @@ fn test_partition_point() {
     assert_eq!(b.partition_point(|&x| x < 7), 2);
     assert_eq!(b.partition_point(|&x| x < 8), 3);
 }
+
+#[test]
+fn is_sorted() {
+    fn expect(set: &IndexSet<i32>, e: [bool; 4]) {
+        assert_eq!(e[0], set.is_sorted());
+        assert_eq!(e[1], set.is_sorted_by(|v1, v2| v1 < v2));
+        assert_eq!(e[2], set.is_sorted_by(|v1, v2| v1 > v2));
+        assert_eq!(e[3], set.is_sorted_by_key(|v| v));
+    }
+
+    let mut set = IndexSet::<i32>::from_iter(0..10);
+    expect(&set, [true, true, false, true]);
+
+    set.replace_index(5, -1).unwrap();
+    expect(&set, [false, false, false, false]);
+}
+
+#[test]
+fn is_sorted_trivial() {
+    fn expect(set: &IndexSet<i32>, e: [bool; 5]) {
+        assert_eq!(e[0], set.is_sorted());
+        assert_eq!(e[1], set.is_sorted_by(|_, _| true));
+        assert_eq!(e[2], set.is_sorted_by(|_, _| false));
+        assert_eq!(e[3], set.is_sorted_by_key(|_| 0f64));
+        assert_eq!(e[4], set.is_sorted_by_key(|_| f64::NAN));
+    }
+
+    let mut set = IndexSet::<i32>::default();
+    expect(&set, [true, true, true, true, true]);
+
+    set.insert(0);
+    expect(&set, [true, true, true, true, true]);
+
+    set.insert(1);
+    expect(&set, [true, true, false, true, false]);
+
+    set.reverse();
+    expect(&set, [false, true, false, true, false]);
+}