In a recent announcement by Steam, users can now play their games via their smartphones via Steam Link for Mobile. Though it's not as easy as originally planned. Apple has rejected the iOS version of the app.
Valve originally intended for the Steam Link mobile app to launch on May 21 for Android and iOS. Any device with a 5Ghz wifi or wired ethernet connection could connect to a PC running Steam and play their games. As long as you have a controller of some kind connected as well. The app is available for Android right now.
There's been a complication with the iOS version, however. On May 24, Steam announced on Twitter that while the app was initially accepted, it was later rejected by Apple, citing business conflicts with app guidelines that had allegedly not been realized by the original review team. Valve attempted to repeal the decision, stating that numerous apps on the iTunes App Store similar in nature to Steam Link already exist. The repeal was also denied.
No word on whether the app will make it to the App Store in the future.