The Music app in iOS 10 adopts a new card-like appearance: Now Playing screen slides up, while the view below in the hierarchy zooms out, protruding slightly at the top of t
Ok, I'll try to give you a compact solution with a minimum of code.
Fast solution.
You need to present a controller modally with modalPresentationStyle-property set to .overCurrentContext. You can set the value before preset(controller:...)-method get called or in prepare(for:...)-one if it's a segue transition. For sliding up use modalTransitionStyle set to .coverVertical.
To "zoom out" source view just update its bounds in viewWill(Diss)appear-methods. In most of cases this will work.
Don't forget to set your modal controller background view transparent so the underlying view still be visible.
Sliding up/down smoothly. You need to setup a transition between the controllers in a proper way. If you look closer to Apple music app, you'll see a way to hide top controller with slide down gesture. You can customise your view (dis)appearance too. Take a look at this article. It uses UIKit-methods only. Unfortunately this way requires lots of code, but you can use 3rd party libraries to setup transitions. Like this one.