diff --git a/src/PriorityQueue.php b/src/PriorityQueue.php
new file mode 100644
index 00000000..2e6a8395
--- /dev/null
+++ b/src/PriorityQueue.php
@@ -0,0 +1,187 @@
+<?php declare(strict_types=1);
+
+namespace Amp;
+
+/**
+ * Uses a binary tree stored in an array to implement a heap.
+ *
+ * @template T of int|string
+ */
+final class PriorityQueue
+{
+    /** @var array<int, object{key: T, priority: int}> */
+    private array $data = [];
+
+    /** @var array<T, int> */
+    private array $pointers = [];
+
+    /**
+     * Inserts the key into the queue with the given priority or updates the priority if the key
+     * already exists in the queue.
+     *
+     * Time complexity: O(log(n)).
+     *
+     * @param T $key
+     */
+    public function insert(int|string $key, int $priority): void
+    {
+        if (isset($this->pointers[$key])) {
+            $node = $this->pointers[$key];
+            $entry = $this->data[$node];
+
+            $previous = $entry->priority;
+            $entry->priority = $priority;
+
+            // Nothing to be done if priorities are equal.
+            if ($previous < $priority) {
+                $this->heapifyDown($node);
+            } elseif ($previous > $priority) {
+                $this->heapifyUp($node);
+            }
+
+            return;
+        }
+
+        $entry = new class($key, $priority) {
+            public function __construct(
+                public readonly int|string $key,
+                public int $priority,
+            ) {
+            }
+        };
+
+        $node = \count($this->data);
+        $this->data[$node] = $entry;
+        $this->pointers[$key] = $node;
+
+        $this->heapifyUp($node);
+    }
+
+    /**
+     * Removes the given key from the queue.
+     *
+     * Time complexity: O(log(n)).
+     *
+     * @param T $key
+     */
+    public function remove(int|string $key): void
+    {
+        if (!isset($this->pointers[$key])) {
+            return;
+        }
+
+        $this->removeAndRebuild($this->pointers[$key]);
+    }
+
+    /**
+     * Deletes and returns the data at the top of the queue if the priority is less than the priority given.
+     *
+     * Time complexity: O(log(n)).
+     *
+     * @param int $priority Extract data with a priority less than the given priority.
+     *
+     * @return T|null
+     */
+    public function extract(int $priority = \PHP_INT_MAX): int|string|null
+    {
+        $data = $this->data[0] ?? null;
+        if ($data === null || $data->priority > $priority) {
+            return null;
+        }
+
+        $this->removeAndRebuild(0);
+
+        return $data->key;
+    }
+
+    /**
+     * Returns the data at top of the heap or null if empty. Time complexity: O(1).
+     *
+     * @return T|null
+     */
+    public function peekData(): int|string|null
+    {
+        return ($this->data[0] ?? null)?->key;
+    }
+
+    /**
+     * Returns the priority at top of the heap or null if empty. Time complexity: O(1).
+     */
+    public function peekPriority(): ?int
+    {
+        return ($this->data[0] ?? null)?->priority;
+    }
+
+    public function isEmpty(): bool
+    {
+        return empty($this->data);
+    }
+
+    /**
+     * @param int $node Rebuild the data array from the given node upward.
+     */
+    private function heapifyUp(int $node): void
+    {
+        $entry = $this->data[$node];
+        while ($node !== 0 && $entry->priority < $this->data[$parent = ($node - 1) >> 1]->priority) {
+            $this->swap($node, $parent);
+            $node = $parent;
+        }
+    }
+
+    /**
+     * @param int $node Rebuild the data array from the given node downward.
+     */
+    private function heapifyDown(int $node): void
+    {
+        $length = \count($this->data);
+        while (($child = ($node << 1) + 1) < $length) {
+            if ($this->data[$child]->priority < $this->data[$node]->priority
+                && ($child + 1 >= $length || $this->data[$child]->priority < $this->data[$child + 1]->priority)
+            ) {
+                // Left child is less than parent and right child.
+                $swap = $child;
+            } elseif ($child + 1 < $length && $this->data[$child + 1]->priority < $this->data[$node]->priority) {
+                // Right child is less than parent and left child.
+                $swap = $child + 1;
+            } else { // Left and right child are greater than parent.
+                break;
+            }
+
+            $this->swap($node, $swap);
+            $node = $swap;
+        }
+    }
+
+    private function swap(int $left, int $right): void
+    {
+        $temp = $this->data[$left];
+
+        $this->data[$left] = $this->data[$right];
+        $this->pointers[$this->data[$right]->key] = $left;
+
+        $this->data[$right] = $temp;
+        $this->pointers[$temp->key] = $right;
+    }
+
+    /**
+     * @param int $node Remove the given node and then rebuild the data array.
+     */
+    private function removeAndRebuild(int $node): void
+    {
+        $length = \count($this->data) - 1;
+        $id = $this->data[$node]->key;
+        $left = $this->data[$node] = $this->data[$length];
+        $this->pointers[$left->key] = $node;
+        unset($this->data[$length], $this->pointers[$id]);
+
+        if ($node < $length) { // don't need to do anything if we removed the last element
+            $parent = ($node - 1) >> 1;
+            if ($parent >= 0 && $this->data[$node]->priority < $this->data[$parent]->priority) {
+                $this->heapifyUp($node);
+            } else {
+                $this->heapifyDown($node);
+            }
+        }
+    }
+}
diff --git a/test/PriorityQueueTest.php b/test/PriorityQueueTest.php
new file mode 100644
index 00000000..dee64fbe
--- /dev/null
+++ b/test/PriorityQueueTest.php
@@ -0,0 +1,64 @@
+<?php declare(strict_types=1);
+
+namespace Amp;
+
+class PriorityQueueTest extends TestCase
+{
+    public function provideTestValues(): iterable
+    {
+        return [
+            [100, 0, 0],
+            [100, 0, 10],
+            [100, 10, 0],
+            [100, 10, 10],
+            [1000, 25, 25],
+            [1000, 100, 100],
+            [10, 0, 0],
+            [10, 3, 3],
+            [5, 1, 2],
+        ];
+    }
+
+    /**
+     * @dataProvider provideTestValues
+     */
+    public function testOrdering(int $count, int $toRemove, $toIncrement): void
+    {
+        $priorities = \range(0, $count - 1);
+        \shuffle($priorities);
+
+        $queue = new PriorityQueue();
+
+        foreach ($priorities as $key => $priority) {
+            $queue->insert($key, $priority);
+        }
+
+        for ($i = 0; $i < $toIncrement; ++$i) {
+            $index = \random_int(0, $count - 1);
+            $queue->insert($index, $count + $i);
+            $priorities[$index] = $count + $i;
+        }
+
+        $i = 0;
+        while ($i < $toRemove) {
+            $index = \random_int(0, $count - 1);
+            if (!isset($priorities[$index])) {
+                continue;
+            }
+
+            unset($priorities[$index]);
+            $queue->remove($index);
+            ++$i;
+        }
+
+        $output = [];
+        while (($extracted = $queue->extract()) !== null) {
+            $output[] = $extracted;
+        }
+
+        \asort($priorities);
+
+        self::assertCount(\count($priorities), $output);
+        self::assertSame(\array_keys($priorities), $output);
+    }
+}