diff --git a/library/alloc/src/collections/binary_heap/extract_if.rs b/library/alloc/src/collections/binary_heap/extract_if.rs
new file mode 100644
index 0000000000000..3aa50fc67e097
--- /dev/null
+++ b/library/alloc/src/collections/binary_heap/extract_if.rs
@@ -0,0 +1,89 @@
+use core::fmt;
+use core::iter::FusedIterator;
+use core::mem::ManuallyDrop;
+
+use super::BinaryHeap;
+use crate::alloc::{Allocator, Global};
+
+/// An iterator which uses a closure to determine if an element should be removed.
+///
+/// This struct is created by [`BinaryHeap::extract_if`].
+/// See its documentation for more.
+///
+/// # Example
+///
+/// ```
+/// #![feature(binary_heap_extract_if)]
+/// use crate::alloc::collections::BinaryHeap;
+///
+/// let mut heap: BinaryHeap<u32> = (0..128).collect();
+/// let iter: Vec<u32> = heap.extract_if(|x| *x % 2 == 0).collect();
+#[unstable(feature = "binary_heap_extract_if", issue = "154721")]
+#[must_use = "iterators are lazy and do nothing unless consumed; \
+    use `retain_mut` or `extract_if().for_each(drop)` to remove and discard elements"]
+pub struct ExtractIf<
+    'a,
+    T: Ord,
+    F,
+    #[unstable(feature = "allocator_api", issue = "32838")] A: Allocator = Global,
+> {
+    heap_ptr: *mut BinaryHeap<T, A>,
+    extract_if: ManuallyDrop<super::vec::ExtractIf<'a, T, F, A>>,
+}
+
+impl<T: Ord, F, A: Allocator> ExtractIf<'_, T, F, A>
+where
+    F: FnMut(&mut T) -> bool,
+{
+    pub(super) fn new<'a>(heap: &'a mut BinaryHeap<T, A>, predicate: F) -> ExtractIf<'a, T, F, A> {
+        // We need to keep a reference around to the heap so that we can
+        let heap_ptr: *mut BinaryHeap<T, A> = heap;
+        let extract_if = ManuallyDrop::new(heap.data.extract_if(.., predicate));
+
+        ExtractIf { heap_ptr, extract_if }
+    }
+}
+
+#[unstable(feature = "binary_heap_extract_if", issue = "154721")]
+impl<T: Ord, F, A: Allocator> Iterator for ExtractIf<'_, T, F, A>
+where
+    F: FnMut(&mut T) -> bool,
+{
+    type Item = T;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        self.extract_if.next()
+    }
+}
+
+#[unstable(feature = "binary_heap_extract_if", issue = "154721")]
+impl<'a, T: Ord, F, A: Allocator> Drop for ExtractIf<'a, T, F, A> {
+    fn drop(&mut self) {
+        // SAFETY: We need to drop this before we rebuild the heap so that its descructor resets the vec info
+        //      We also are only calling this hear during the drop of ExtractIf and then never using it again
+        unsafe {
+            ManuallyDrop::drop(&mut self.extract_if);
+        }
+
+        // SAFETY: We only generate this ptr from a reference so we know that it is never null
+        let heap = unsafe { self.heap_ptr.as_mut_unchecked() };
+
+        // Removing some items from the heap almost certainly has invalidated its invariants, we need to fix this up here
+        heap.rebuild();
+    }
+}
+
+#[unstable(feature = "binary_heap_extract_if", issue = "154721")]
+impl<T: Ord, F, A: Allocator> FusedIterator for ExtractIf<'_, T, F, A> where F: FnMut(&mut T) -> bool
+{}
+
+#[unstable(feature = "binary_heap_extract_if", issue = "154721")]
+impl<T: Ord, F, A> fmt::Debug for ExtractIf<'_, T, F, A>
+where
+    T: fmt::Debug,
+    A: Allocator,
+{
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.debug_struct("ExtractIf").finish_non_exhaustive()
+    }
+}
diff --git a/library/alloc/src/collections/binary_heap/mod.rs b/library/alloc/src/collections/binary_heap/mod.rs
index 4ddfcde57280e..c7ad4430d71c3 100644
--- a/library/alloc/src/collections/binary_heap/mod.rs
+++ b/library/alloc/src/collections/binary_heap/mod.rs
@@ -150,6 +150,11 @@ use core::num::NonZero;
 use core::ops::{Deref, DerefMut};
 use core::{fmt, ptr};
 
+#[unstable(feature = "binary_heap_extract_if", issue = "154721")]
+pub use self::extract_if::ExtractIf;
+
+mod extract_if;
+
 use crate::alloc::Global;
 use crate::collections::TryReserveError;
 use crate::slice;
@@ -1039,6 +1044,19 @@ impl<T: Ord, A: Allocator> BinaryHeap<T, A> {
         DrainSorted { inner: self }
     }
 
+    /// Creates an iterator which uses a closure to determine if an element should be removed.
+    /// The items are checked in sorted order
+    ///
+    /// If the closure returns `true`, the element is marked to be removed and yielded
+    #[unstable(feature = "binary_heap_extract_if", issue = "154721")]
+    #[must_use]
+    pub fn extract_if<F>(&mut self, predicate: F) -> ExtractIf<'_, T, F, A>
+    where
+        F: FnMut(&mut T) -> bool,
+    {
+        ExtractIf::new(self, predicate)
+    }
+
     /// Retains only the elements specified by the predicate.
     ///
     /// In other words, remove all elements `e` for which `f(&e)` returns
diff --git a/library/alloctests/tests/collections/binary_heap.rs b/library/alloctests/tests/collections/binary_heap.rs
index e1484c32a4f8a..c712918a98b35 100644
--- a/library/alloctests/tests/collections/binary_heap.rs
+++ b/library/alloctests/tests/collections/binary_heap.rs
@@ -590,3 +590,65 @@ fn panic_safe() {
         }
     }
 }
+
+#[test]
+fn given_a_binary_heap_can_create_an_extract_if_iterator() {
+    let mut heap: BinaryHeap<usize> = BinaryHeap::new();
+    let iter = heap.extract_if(|_| unreachable!("there's nothing to decide on"));
+
+    iter.for_each(drop);
+    assert!(heap.is_empty())
+}
+
+#[test]
+fn given_some_binary_heap_with_one_item_when_extracting_if_true_extracts_all_items() {
+    let mut heap: BinaryHeap<usize> = BinaryHeap::new();
+    heap.push(10);
+    let v: Vec<usize> = heap.extract_if(|_| true).collect();
+
+    assert!(heap.is_empty());
+    assert_eq!(v, vec![10]);
+}
+
+#[test]
+fn given_some_binary_heap_with_three_items_when_extracting_if_true_extracts_all_items_in_arbitrary_order()
+ {
+    let mut heap = BinaryHeap::new();
+    heap.push(10);
+    heap.push(15);
+    heap.push(11);
+    let v: Vec<_> = heap.extract_if(|_| true).collect();
+
+    assert!(heap.is_empty());
+    assert_eq!(v, vec![15, 10, 11]);
+}
+
+#[test]
+fn given_some_binary_heap_with_some_items_when_extracting_if_even_extracts_just_even_items() {
+    let mut heap = BinaryHeap::new();
+    heap.push(10);
+    heap.push(15);
+    heap.push(11);
+    let v: Vec<_> = heap.extract_if(|&mut x| x % 2 == 0).collect();
+
+    assert_eq!(v, vec![10]);
+    assert_eq!(heap.pop(), Some(15));
+    assert_eq!(heap.pop(), Some(11));
+    assert_eq!(heap.pop(), None);
+}
+
+#[test]
+fn given_some_binary_heap_with_some_items_when_extracting_if_when_dropping_without_iterating_leaves_heap_in_valid_state()
+ {
+    let mut heap = BinaryHeap::new();
+    heap.push(10);
+    heap.push(15);
+    heap.push(11);
+
+    drop(heap.extract_if(|&mut x| x % 2 == 0));
+
+    assert_eq!(heap.pop(), Some(15));
+    assert_eq!(heap.pop(), Some(11));
+    assert_eq!(heap.pop(), Some(10));
+    assert_eq!(heap.pop(), None);
+}
diff --git a/library/alloctests/tests/lib.rs b/library/alloctests/tests/lib.rs
index 699a5010282b0..61d696b33020a 100644
--- a/library/alloctests/tests/lib.rs
+++ b/library/alloctests/tests/lib.rs
@@ -1,4 +1,5 @@
 #![feature(allocator_api)]
+#![feature(binary_heap_extract_if)]
 #![feature(binary_heap_pop_if)]
 #![feature(const_heap)]
 #![feature(deque_extend_front)]