Remote control/remote desktop on Android - e.g teamviewer

I am wondering how teamviewer for android and simple applications work. For instance, teamviewer claims on its webpage, that they can remotely control devices with Android from Samsung, Lenovo, Sony, HTC, and many others.

I know, that samsung safe devices have some API for this, but what about others? How it is possible to remotely control non-rooted Android device?

Appreciate any ideas.