diff --git a/lib/Future.php b/lib/Future.php
index 1c31c08..b76261c 100644
--- a/lib/Future.php
+++ b/lib/Future.php
@@ -107,6 +107,14 @@ final class Future
         return $this->state->isComplete();
     }
 
+    /**
+     * Do not forward unhandled errors to the event loop handler.
+     */
+    public function ignore(): void
+    {
+        $this->state->ignore();
+    }
+
     /**
      * Awaits the operation to complete.
      *
diff --git a/lib/Internal/FutureState.php b/lib/Internal/FutureState.php
index 6688b39..30a1ee9 100644
--- a/lib/Internal/FutureState.php
+++ b/lib/Internal/FutureState.php
@@ -2,6 +2,7 @@
 
 namespace Amp\Internal;
 
+use Amp\UnhandledFutureError;
 use Revolt\EventLoop\Loop;
 use Amp\Future;
 
@@ -17,8 +18,10 @@ final class FutureState
 
     private bool $complete = false;
 
+    private bool $handled = false;
+
     /**
-     * @var array<string, (callable(?\Throwable, ?T, string): void)>
+     * @var array<string, callable(?\Throwable, ?T, string): void>
      */
     private array $callbacks = [];
 
@@ -29,12 +32,21 @@ final class FutureState
 
     private ?\Throwable $throwable = null;
 
+    public function __destruct()
+    {
+        if ($this->throwable && !$this->handled) {
+            $throwable = new UnhandledFutureError($this->throwable);
+            Loop::queue(static fn () => throw $throwable);
+        }
+    }
+
     /**
      * Registers a callback to be notified once the operation is complete or errored.
      *
      * The callback is invoked directly from the event loop context, so suspension within the callback is not possible.
      *
-     * @param (callable(?\Throwable, ?T, string): void) $callback Callback invoked on error / successful completion of the future.
+     * @param callable(?\Throwable, ?T, string): void $callback Callback invoked on error / successful completion of
+     * the future.
      *
      * @return string Identifier that can be used to cancel interest for this future.
      */
@@ -42,6 +54,8 @@ final class FutureState
     {
         $id = self::$nextId++;
 
+        $this->handled = true; // Even if unsubscribed later, consider the future handled.
+
         if ($this->complete) {
             Loop::queue($callback, $this->throwable, $this->result, $id);
         } else {
@@ -105,6 +119,14 @@ final class FutureState
         return $this->complete;
     }
 
+    /**
+     * Suppress the exception thrown to the loop error handler if and operation error is not handled by a callback.
+     */
+    public function ignore(): void
+    {
+        $this->handled = true;
+    }
+
     private function invokeCallbacks(): void
     {
         $this->complete = true;
diff --git a/lib/UnhandledFutureError.php b/lib/UnhandledFutureError.php
new file mode 100644
index 0000000..017cf56
--- /dev/null
+++ b/lib/UnhandledFutureError.php
@@ -0,0 +1,18 @@
+<?php
+
+namespace Amp;
+
+/**
+ * Will be thrown to the event loop error handler in case a future exception is not handled.
+ */
+final class UnhandledFutureError extends \Error
+{
+    public function __construct(?\Throwable $previous = null)
+    {
+        $message = 'Unhandled future error: "' . $previous->getMessage()
+            . '"; Await the Future with Future::await() before the future is destroyed or use '
+            . 'Future::ignore() to suppress this exception';
+
+        parent::__construct($message, 0, $previous);
+    }
+}
diff --git a/test/Future/AllTest.php b/test/Future/AllTest.php
index c867e4c..1140789 100644
--- a/test/Future/AllTest.php
+++ b/test/Future/AllTest.php
@@ -8,6 +8,7 @@ use Amp\Future;
 use Amp\TimeoutCancellationToken;
 use PHPUnit\Framework\TestCase;
 use Revolt\EventLoop\Loop;
+use function Amp\delay;
 use function Amp\Future\all;
 
 class AllTest extends TestCase
@@ -39,6 +40,17 @@ class AllTest extends TestCase
         all([Future::error(new \Exception('foo')), Future::complete(2)]);
     }
 
+    public function testTwoThrowingWithOneLater(): void
+    {
+        $this->expectException(\Exception::class);
+        $this->expectExceptionMessage('foo');
+
+        $deferred = new Deferred;
+        Loop::delay(0.1, static fn () => $deferred->error(new \Exception('bar')));
+
+        all([Future::error(new \Exception('foo')), $deferred->getFuture()]);
+    }
+
     public function testTwoGeneratorThrows(): void
     {
         $this->expectException(\Exception::class);
diff --git a/test/Future/FutureTest.php b/test/Future/FutureTest.php
index 200c0ee..e9509e3 100644
--- a/test/Future/FutureTest.php
+++ b/test/Future/FutureTest.php
@@ -6,14 +6,16 @@ use Amp\CancellationTokenSource;
 use Amp\CancelledException;
 use Amp\Deferred;
 use Amp\Future;
+use Amp\PHPUnit\AsyncTestCase;
+use Amp\PHPUnit\LoopCaughtException;
+use Amp\PHPUnit\TestException;
 use Amp\TimeoutCancellationToken;
-use PHPUnit\Framework\TestCase;
 use Revolt\EventLoop\Loop;
 use function Amp\coroutine;
 use function Amp\delay;
 use function Revolt\EventLoop\queue;
 
-class FutureTest extends TestCase
+class FutureTest extends AsyncTestCase
 {
     public function testIterate(): void
     {
@@ -154,8 +156,43 @@ class FutureTest extends TestCase
 
         $deferred->complete(1);
         $source->cancel();
+    }
 
-        delay(0.01); // Tick the event loop to enter defer callback.
+
+    public function testUnhandledError(): void
+    {
+        $deferred = new Deferred;
+        $deferred->error(new TestException);
+        unset($deferred);
+
+        $this->expectException(LoopCaughtException::class);
+    }
+
+    public function testUnhandledErrorFromFutureError(): void
+    {
+        $future = Future::error(new TestException);
+        unset($future);
+
+        $this->expectException(LoopCaughtException::class);
+    }
+
+    public function testIgnoringUnhandledErrors(): void
+    {
+        $deferred = new Deferred;
+        $deferred->getFuture()->ignore();
+        $deferred->error(new TestException);
+        unset($deferred);
+
+        Loop::setErrorHandler($this->createCallback(0));
+    }
+
+    public function testIgnoreUnhandledErrorFromFutureError(): void
+    {
+        $future = Future::error(new TestException);
+        $future->ignore();
+        unset($future);
+
+        Loop::setErrorHandler($this->createCallback(0));
     }
 
     /**