Index: src/wp-includes/default-filters.php
===================================================================
--- src/wp-includes/default-filters.php	(revision 36603)
+++ src/wp-includes/default-filters.php	(working copy)
@@ -342,6 +342,7 @@
 
 // Default authentication filters
 add_filter( 'authenticate', 'wp_authenticate_username_password',  20, 3 );
+add_filter( 'authenticate', 'wp_authenticate_email_password',     20, 3 );
 add_filter( 'authenticate', 'wp_authenticate_spam_check',         99    );
 add_filter( 'determine_current_user', 'wp_validate_auth_cookie'          );
 add_filter( 'determine_current_user', 'wp_validate_logged_in_cookie', 20 );
Index: src/wp-includes/pluggable.php
===================================================================
--- src/wp-includes/pluggable.php	(revision 36603)
+++ src/wp-includes/pluggable.php	(working copy)
@@ -548,7 +548,7 @@
  *
  * @since 2.5.0
  *
- * @param string $username User's username.
+ * @param string $username User's username or email address.
  * @param string $password User's password.
  * @return WP_User|WP_Error WP_User object if the credentials are valid,
  *                          otherwise WP_Error.
@@ -575,7 +575,7 @@
 	if ( $user == null ) {
 		// TODO what should the error message be? (Or would these even happen?)
 		// Only needed if all authentication handlers fail to return anything.
-		$user = new WP_Error('authentication_failed', __('<strong>ERROR</strong>: Invalid username or incorrect password.'));
+		$user = new WP_Error( 'authentication_failed', __( '<strong>ERROR</strong>: Invalid username, email address or incorrect password.' ) );
 	}
 
 	$ignore_codes = array('empty_username', 'empty_password');
Index: src/wp-includes/user.php
===================================================================
--- src/wp-includes/user.php	(revision 36603)
+++ src/wp-includes/user.php	(working copy)
@@ -174,6 +174,79 @@
 }
 
 /**
+ * Authenticate the user using the email and password.
+ *
+ * @since 4.5.0
+ *
+ * @param WP_User|WP_Error|null $user     WP_User or WP_Error object if a previous
+ *                                        callback failed authentication.
+ * @param string                $email    Email address for authentication.
+ * @param string                $password Password for authentication.
+ * @return WP_User|WP_Error WP_User on success, WP_Error on failure.
+ */
+function wp_authenticate_email_password( $user, $email, $password ) {
+	if ( $user instanceof WP_User ) {
+		return $user;
+	}
+
+	if ( empty( $email ) || empty( $password ) ) {
+		if ( is_wp_error( $user ) ) {
+			return $user;
+		}
+
+		$error = new WP_Error();
+
+		if ( empty( $email ) ) {
+			$error->add( 'empty_username', __( '<strong>ERROR</strong>: The email field is empty.' ) );
+		}
+
+		if ( empty( $password ) ) {
+			$error->add( 'empty_password', __( '<strong>ERROR</strong>: The password field is empty.' ) );
+		}
+
+		return $error;
+	}
+
+	if ( ! is_email( $email ) ) {
+		return $user;
+	}
+
+	$user = get_user_by( 'email', $email );
+
+	if ( ! $user ) {
+		return new WP_Error( 'invalid_email',
+			__( '<strong>ERROR</strong>: Invalid email address.' ) .
+			' <a href="' . wp_lostpassword_url() . '">' .
+			__( 'Lost your password?' ) .
+			'</a>'
+		);
+	}
+
+	/** This filter is documented in wp-includes/user.php */
+	$user = apply_filters( 'wp_authenticate_user', $user, $password );
+
+	if ( is_wp_error( $user ) ) {
+		return $user;
+	}
+
+	if ( ! wp_check_password( $password, $user->user_pass, $user->ID ) ) {
+		return new WP_Error( 'incorrect_password',
+			sprintf(
+			/* translators: %s: email address */
+				__( '<strong>ERROR</strong>: The password you entered for the email address %s is incorrect.' ),
+				'<strong>' . $email . '</strong>'
+			) .
+			' <a href="' . wp_lostpassword_url() . '">' .
+			__( 'Lost your password?' ) .
+			'</a>'
+		);
+	}
+
+	return $user;
+}
+
+
+/**
  * Authenticate the user using the WordPress auth cookie.
  *
  * @since 2.8.0
Index: src/wp-login.php
===================================================================
--- src/wp-login.php	(revision 36603)
+++ src/wp-login.php	(working copy)
@@ -529,7 +529,7 @@
 
 <form name="lostpasswordform" id="lostpasswordform" action="<?php echo esc_url( network_site_url( 'wp-login.php?action=lostpassword', 'login_post' ) ); ?>" method="post">
 	<p>
-		<label for="user_login" ><?php _e('Username or Email:') ?><br />
+		<label for="user_login" ><?php _e('Username or email') ?><br />
 		<input type="text" name="user_login" id="user_login" class="input" value="<?php echo esc_attr($user_login); ?>" size="20" /></label>
 	</p>
 	<?php
@@ -756,7 +756,13 @@
 	// If the user wants ssl but the session is not ssl, force a secure cookie.
 	if ( !empty($_POST['log']) && !force_ssl_admin() ) {
 		$user_name = sanitize_user($_POST['log']);
-		if ( $user = get_user_by('login', $user_name) ) {
+		$user = get_user_by( 'login', $user_name );
+
+		if ( ! $user && strpos( $user_name, '@' ) ) {
+			$user = get_user_by( 'email', $user_name );
+		}
+
+		if ( $user ) {
 			if ( get_user_option('use_ssl', $user->ID) ) {
 				$secure_cookie = true;
 				force_ssl_admin(true);
@@ -882,7 +888,7 @@
 
 <form name="loginform" id="loginform" action="<?php echo esc_url( site_url( 'wp-login.php', 'login_post' ) ); ?>" method="post">
 	<p>
-		<label for="user_login"><?php _e('Username') ?><br />
+		<label for="user_login"><?php _e('Username or email') ?><br />
 		<input type="text" name="log" id="user_login"<?php echo $aria_describedby_error; ?> class="input" value="<?php echo esc_attr( $user_login ); ?>" size="20" /></label>
 	</p>
 	<p>
Index: tests/phpunit/tests/auth.php
===================================================================
--- tests/phpunit/tests/auth.php	(revision 36603)
+++ tests/phpunit/tests/auth.php	(working copy)
@@ -311,4 +311,21 @@
 		$check = check_password_reset_key( '', $this->user->user_login );
 		$this->assertInstanceOf( 'WP_Error', $check );
 	}
+
+	/**
+	 * Ensure users can log in using both their username and their email address.
+	 *
+	 * @ticket 9568
+	 */
+	function test_log_in_using_email() {
+		$user_args = array(
+			'user_login' => 'johndoe',
+			'user_email' => 'mail@example.com',
+			'user_pass'  => 'password',
+		);
+		$this->factory->user->create( $user_args );
+
+		$this->assertInstanceOf( 'WP_User', wp_authenticate( $user_args['user_email'], $user_args['user_pass'] ) );
+		$this->assertInstanceOf( 'WP_User', wp_authenticate( $user_args['user_login'], $user_args['user_pass'] ) );
+	}
 }