diff --git a/src/JWK.php b/src/JWK.php
index c7eff8ae..873ab41a 100644
--- a/src/JWK.php
+++ b/src/JWK.php
@@ -31,6 +31,12 @@ class JWK
         // 'P-521' => '1.3.132.0.35', // Len: 132 (not supported)
     ];
 
+    // For keys with "kty" equal to "OKP" (Octet Key Pair), the "crv" parameter must contain the key subtype.
+    // This library supports the following subtypes:
+    private const OKP_SUBTYPES = [
+        'Ed25519' => true, // RFC 8037
+    ];
+
     /**
      * Parse a set of JWK keys
      *
@@ -145,8 +151,28 @@ public static function parseKey(array $jwk, string $defaultAlg = null): ?Key
 
                 $publicKey = self::createPemFromCrvAndXYCoordinates($jwk['crv'], $jwk['x'], $jwk['y']);
                 return new Key($publicKey, $jwk['alg']);
+            case 'OKP':
+                if (isset($jwk['d'])) {
+                    // The key is actually a private key
+                    throw new UnexpectedValueException('Key data must be for a public key');
+                }
+
+                if (!isset($jwk['crv'])) {
+                    throw new UnexpectedValueException('crv not set');
+                }
+
+                if (empty(self::OKP_SUBTYPES[$jwk['crv']])) {
+                    throw new DomainException('Unrecognised or unsupported OKP key subtype');
+                }
+
+                if (empty($jwk['x'])) {
+                    throw new UnexpectedValueException('x not set');
+                }
+
+                // This library works internally with EdDSA keys (Ed25519) encoded in standard base64.
+                $publicKey = JWT::convertBase64urlToBase64($jwk['x']);
+                return new Key($publicKey, $jwk['alg']);
             default:
-                // Currently only RSA is supported
                 break;
         }
 
diff --git a/src/JWT.php b/src/JWT.php
index c83ff099..dded75f7 100644
--- a/src/JWT.php
+++ b/src/JWT.php
@@ -215,7 +215,7 @@ public static function encode(
      *
      * @param string $msg  The message to sign
      * @param string|resource|OpenSSLAsymmetricKey|OpenSSLCertificate  $key  The secret key.
-     * @param string $alg  Supported algorithms are 'ES384','ES256', 'ES256K', 'HS256',
+     * @param string $alg  Supported algorithms are 'EdDSA', 'ES384', 'ES256', 'ES256K', 'HS256',
      *                    'HS384', 'HS512', 'RS256', 'RS384', and 'RS512'
      *
      * @return string An encrypted message
@@ -278,7 +278,7 @@ public static function sign(
      *
      * @param string $msg         The original message (header and body)
      * @param string $signature   The original signature
-     * @param string|resource|OpenSSLAsymmetricKey|OpenSSLCertificate  $keyMaterial For HS*, a string key works. for RS*, must be an instance of OpenSSLAsymmetricKey
+     * @param string|resource|OpenSSLAsymmetricKey|OpenSSLCertificate  $keyMaterial For Ed*, ES*, HS*, a string key works. for RS*, must be an instance of OpenSSLAsymmetricKey
      * @param string $alg         The algorithm
      *
      * @return bool
@@ -399,13 +399,28 @@ public static function jsonEncode(array $input): string
      * @throws InvalidArgumentException invalid base64 characters
      */
     public static function urlsafeB64Decode(string $input): string
+    {
+        return \base64_decode(self::convertBase64UrlToBase64($input));
+    }
+
+    /**
+     * Convert a string in the base64url (URL-safe Base64) encoding to standard base64.
+     *
+     * @param string $input A Base64 encoded string with URL-safe characters (-_ and no padding)
+     *
+     * @return string A Base64 encoded string with standard characters (+/) and padding (=), when
+     * needed.
+     *
+     * @see https://www.rfc-editor.org/rfc/rfc4648
+     */
+    public static function convertBase64UrlToBase64(string $input): string
     {
         $remainder = \strlen($input) % 4;
         if ($remainder) {
             $padlen = 4 - $remainder;
             $input .= \str_repeat('=', $padlen);
         }
-        return \base64_decode(\strtr($input, '-_', '+/'));
+        return \strtr($input, '-_', '+/');
     }
 
     /**
diff --git a/tests/JWKTest.php b/tests/JWKTest.php
index 93afea70..4e1b0c67 100644
--- a/tests/JWKTest.php
+++ b/tests/JWKTest.php
@@ -151,6 +151,7 @@ public function provideDecodeByJwkKeySet()
         return [
             ['rsa1-private.pem', 'rsa-jwkset.json', 'RS256'],
             ['ecdsa256-private.pem', 'ec-jwkset.json', 'ES256'],
+            ['ed25519-1.sec', 'ed25519-jwkset.json', 'EdDSA'],
         ];
     }
 
diff --git a/tests/data/ed25519-jwkset.json b/tests/data/ed25519-jwkset.json
new file mode 100644
index 00000000..186b8e29
--- /dev/null
+++ b/tests/data/ed25519-jwkset.json
@@ -0,0 +1,11 @@
+{
+    "keys": [
+        {
+            "kid": "jwk1",
+            "alg": "EdDSA",
+            "kty": "OKP",
+            "crv": "Ed25519",
+            "x": "uOSJMhbKSG4V5xUHS7B9YHmVg_1yVd-G-Io6oBFhSfY"
+        }
+    ]
+}