diff --git a/README.md b/README.md
index 24c6a7c..902fc81 100644
--- a/README.md
+++ b/README.md
@@ -28,6 +28,9 @@ $optionalString->ifPresent(function (string $value): void { echo $value; });
 if ($optionalString->equals('value')) {
     echo 'It is `value`.';
 }
+
+echo $optionalString->map(fn ($s) => "`{$s}`")->orElse('empty');
+echo $optionalString->flatMap(fn ($s) => OptionalString::of("`{$s}`"))->orElse('empty');
 ```
 
 ### Create and use your own typed optional
diff --git a/src/AbstractOptional.php b/src/AbstractOptional.php
index 4252c3e..59ca093 100644
--- a/src/AbstractOptional.php
+++ b/src/AbstractOptional.php
@@ -63,6 +63,25 @@ public function equals(mixed $obj): bool
         return ($obj === null || static::isSupported($obj)) && $this->value == $obj;
     }
 
+    /**
+     * @template U of mixed
+     *
+     * @param callable(T): self<U> $mapper
+     *
+     * @return self<U>
+     */
+    public function flatMap(callable $mapper): self
+    {
+        if ($this->value !== null) {
+            $mapped = $mapper($this->value);
+            if (!$mapped instanceof self) {
+                throw new InvalidArgumentException('Mapper must return instance of ' . self::class . '.');
+            }
+            return $mapped;
+        }
+        return $this;
+    }
+
     /**
      * @return T
      *
@@ -94,6 +113,27 @@ public function isPresent(): bool
         return $this->wasPresent = $this->value !== null;
     }
 
+    /**
+     * @template U of mixed
+     *
+     * @param callable(T): U $mapper
+     *
+     * @return self<U>
+     */
+    public function map(callable $mapper): self
+    {
+        /** @var callable(T): self<U> $flatMapper */
+        $flatMapper = static function (mixed $value) use ($mapper): self {
+            $mapped = $mapper($value);
+            try {
+                return TypedOptional::of($mapped);
+            } catch (Exception\CouldNotFindTypedOptionalForValue) {
+                return Optional::of($mapped);
+            }
+        };
+        return $this->flatMap($flatMapper);
+    }
+
     /**
      * @param T $other
      *
@@ -140,7 +180,7 @@ public function orElseThrow(callable $exceptionSupplier): mixed
     }
 
     /**
-     * @param T|mixed $value not null
+     * @param mixed $value not null
      */
     abstract protected static function isSupported(mixed $value): bool;
 }
diff --git a/tests/OptionalTest.php b/tests/OptionalTest.php
index 1ad9a96..516eccc 100644
--- a/tests/OptionalTest.php
+++ b/tests/OptionalTest.php
@@ -76,6 +76,20 @@ public static function dataMethodEqualsWorks(): array
         ];
     }
 
+    #[DataProvider('dataMethodFlatMapWorks')]
+    public function testMethodFlatMapWorks(Optional $optional, Optional $expectedResult): void
+    {
+        self::assertTrue($expectedResult->equals($optional->flatMap(fn (string $v): Optional => Optional::of($v . 'x'))));
+    }
+
+    public static function dataMethodFlatMapWorks(): array
+    {
+        return self::makeDataSet([
+            [Optional::of(self::VALUE . 'x')],
+            [Optional::empty()],
+        ]);
+    }
+
     #[DataProvider('dataMethodGetWorks')]
     public function testMethodGetWorks(Optional $optional, ?string $expectedValue, ?string $expectedException): void
     {
@@ -127,6 +141,20 @@ public static function dataMethodIsPresentWorks(): array
         ]);
     }
 
+    #[DataProvider('dataMethodMapWorks')]
+    public function testMethodMapWorks(Optional $optional, mixed $expectedResult): void
+    {
+        self::assertTrue($expectedResult->equals($optional->map(fn (string $v): string => $v . 'x')));
+    }
+
+    public static function dataMethodMapWorks(): array
+    {
+        return self::makeDataSet([
+            [OptionalString::of(self::VALUE . 'x')],
+            [Optional::empty()],
+        ]);
+    }
+
     #[DataProvider('dataMethodOrElseWorks')]
     public function testMethodOrElseWorks(Optional $optional, string $expectedValue): void
     {
diff --git a/tests/ReadmeTest.php b/tests/ReadmeTest.php
index ce0e79d..2c00024 100644
--- a/tests/ReadmeTest.php
+++ b/tests/ReadmeTest.php
@@ -27,6 +27,8 @@ public static function getExpectedOutputsOfPhpExamples(): iterable
                 . 'value'
                 . 'value'
                 . 'It is `value`.'
+                . '`value`'
+                . '`value`'
             ,
             'create--and-use-your-own-typed-optional' => '',
         ];