diff --git a/src/JWK.php b/src/JWK.php
index fab13412..d0ae5630 100644
--- a/src/JWK.php
+++ b/src/JWK.php
@@ -31,6 +31,11 @@ class JWK
         // 'P-521' => '1.3.132.0.35', // Len: 132 (not supported)
     ];
 
+    // 'crv' identifier => JWT 'alg'
+    private const OKP_CURVES = [
+        'Ed25519' => 'EdDSA',
+    ];
+
     /**
      * Parse a set of JWK keys
      *
@@ -93,9 +98,10 @@ public static function parseKey(array $jwk): ?Key
             throw new UnexpectedValueException('JWK must contain a "kty" parameter');
         }
 
-        if (!isset($jwk['alg'])) {
-            // The "alg" parameter is optional in a KTY, but is required for parsing in
-            // this library. Add it manually to your JWK array if it doesn't already exist.
+        $ktyRequiringAlg = ['RSA', 'EC'];
+        if (!isset($jwk['alg']) && \in_array($jwk['kty'], $ktyRequiringAlg, true)) {
+            // The "alg" parameter is optional in a KTY, but is required for parsing certain key
+            // types in this library. Add it manually to your JWK array if it doesn't already exist.
             // @see https://datatracker.ietf.org/doc/html/rfc7517#section-4.4
             throw new UnexpectedValueException('JWK must contain an "alg" parameter');
         }
@@ -137,8 +143,28 @@ public static function parseKey(array $jwk): ?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($jwk['crv'])) {
+                    throw new UnexpectedValueException('crv not set');
+                }
+
+                if (!isset(self::OKP_CURVES[$jwk['crv']])) {
+                    throw new DomainException('Unrecognised or unsupported OKP curve');
+                }
+
+                if (empty($jwk['x'])) {
+                    throw new UnexpectedValueException('x not set');
+                }
+
+                $publicKey = JWT::urlsafeToStandardB64($jwk['x']);
+                $alg = self::OKP_CURVES[$jwk['crv']];
+                return new Key($publicKey, $alg);
             default:
-                // Currently only RSA is supported
                 break;
         }
 
diff --git a/src/JWT.php b/src/JWT.php
index bf064e34..137e8de1 100644
--- a/src/JWT.php
+++ b/src/JWT.php
@@ -207,7 +207,7 @@ 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', 'HS256', 'HS384',
+     * @param string $alg  Supported algorithms are 'EdDSA', 'ES384', 'ES256', 'HS256', 'HS384',
      *                    'HS512', 'RS256', 'RS384', and 'RS512'
      *
      * @return string An encrypted message
@@ -267,7 +267,7 @@ 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
@@ -381,13 +381,26 @@ public static function jsonEncode(array $input): string
      * @throws InvalidArgumentException invalid base64 characters
      */
     public static function urlsafeB64Decode(string $input): string
+    {
+        return \base64_decode(self::urlsafeToStandardB64($input));
+    }
+
+    /**
+     * Convert a string from URL-safe Base64 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.
+     */
+    public static function urlsafeToStandardB64(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 4baefe8a..bbdd7e4c 100644
--- a/tests/JWKTest.php
+++ b/tests/JWKTest.php
@@ -139,6 +139,7 @@ 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..a364af80
--- /dev/null
+++ b/tests/data/ed25519-jwkset.json
@@ -0,0 +1,10 @@
+{
+    "keys": [
+        {
+            "kid": "jwk1",
+            "kty": "OKP",
+            "crv": "Ed25519",
+            "x": "uOSJMhbKSG4V5xUHS7B9YHmVg_1yVd-G-Io6oBFhSfY"
+        }
+    ]
+}