How to display messages when app is running in the foreground?

In order to display incoming messages (both pushed by APNs and pulled from the server) while your application is running in the foreground, you have to:

1. Subscribe to MMNotificationMessageReceived notification:

   //Objective-C
   [[NSNotificationCenter defaultCenter] addObserver: self
                                            selector: @selector(handleNewMessageReceivedNotification:)
                                                name: MMNotificationMessageReceived
                                              object: nil];

   //Swift
   NSNotificationCenter.defaultCenter().addObserver(self,
                                                    selector: #selector(self.handleNewMessageReceivedNotification(_:)),
                                                    name: MMNotificationMessageReceived,
                                                    object: nil)

2. Handle the notifications:

   //Objective-C
   -(void)handleNewMessageReceivedNotification:(NSNotification *)notification {
   	// Only display the message if the application is in the foreground
   	if ([UIApplication sharedApplication].applicationState == UIApplicationStateActive) {
   		id messagePayload = notification.userInfo[MMNotificationKeyMessagePayload];
   		if ([messagePayload isKindOfClass:[NSDictionary class]]) {
   		
   			NSString * messageText = [messagePayload mm_apsAlertBody];
   			
   			// here comes your custom UI, i.e. standard UIAlertController:
   			UIAlertController * alertController = [UIAlertController alertControllerWithTitle:@"New message" message:messageText preferredStyle:UIAlertControllerStyleAlert];
   			[alertController addAction: [UIAlertAction actionWithTitle:@"Dismiss" style:UIAlertActionStyleCancel handler:nil]];
   			UIViewController * presentingVC = [UIApplication sharedApplication].keyWindow.rootViewController;
   			[presentingVC presentViewController:alertController animated:YES completion:nil];
   		}
   	}
   }

   //Swift
   func handleNewMessageReceivedNotification(notification: NSNotification) {
   	// Only display the message if the application is in the foreground
   	guard UIApplication.sharedApplication().applicationState == .Active else {
   		return
   	}
   	guard let userInfo = notification.userInfo,
   		let messagePayload = userInfo[MMNotificationKeyMessagePayload] as? [NSObject : AnyObject],
   		let messageText = messagePayload.mm_apsAlertBody else {
   			return
   	}
   	
   	// here comes your custom UI, i.e. standard UIAlertController:
   	let alertController = UIAlertController(title: "New message", message: messageText, preferredStyle: .Alert)
   	alertController.addAction(UIAlertAction(title: "Dismiss", style: .Cancel, handler: nil))
   	let presentingVC = UIApplication.sharedApplication().keyWindow?.rootViewController {
   		presentingVC.presentViewController(alertController, animated: true, completion: nil)
   	}
   }

mm_apsAlertBody is a public method of NSDictionary extension. In case the receiver is a message payload dictionary¹, it returns the text of the remote message.

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1: A dictionary that contains information related to the remote notification, potentially including a badge number for the app icon, an alert sound, an alert message to display to the user, a notification identifier, and custom data.