How can I respond to push notifications when app isn't running?

I would like our game to communicate with the server via push notifications. I've seen the NotificationServices class, and it seems pretty straightforward how to use it. What isn't clear to me is what happens when a push notification is received while the game is not running. I would like to post a visual notification to the screen when this happens. Is there any way to do this within Unity? Would I have to write a custom iOS plugin to handle this, and then bundle it in to the game somehow? If so, any advice on how to do this?

Thanks.