"Moving" UIViews across UIViewControllers in custom transition?

You know how in some apps, when the app enters a custom transition between two UIViewControllers, the animation makes it seem as if a UIView is moving "from" a UIViewController across "to" the appearing UIViewController? Like in the Duolingo app, when you tap a lesson group on the main screen, the icon of the lesson group magnifies and becomes the "header" of the lesson group page. How do we do that? How do we "share" UIViews between UIViewControllers in custom transitions? (Assuming that we use the iOS 8 APIs such as UIPresentationController and UIViewControllerAnimatedTransitioning.)