Play your Steam games on any Android device with Steam Link, the official Valve app for Android. That being said, it's basically a streaming tool, so you'll need a PC running the game for the app to function.
Steam Link simply mirrors your computer screen to your Android device, so you have to pair your device to a computer with an installed Steam client to use the app, as well as a high speed WiFi connection, and if possible, a wired internet connection to your PC.
Thanks to the Valve controller's latest firmware update, you can a pair a Steam Controller to your smartphone and use to play games on Steam Link, but you could use any bluetooth control system. Although mouse clicks are replaced by tapping on the screen, games that require a joystick require a physical controller.
Play all your favorite steam titles away from your PC with the interesting app Steam Link, that has basically all the same features as the hardware it's named after.
