Last night, Valve launched the Steam Link iOS app that lets you stream your steam library to your iPhone. You can grab the app, for free, here. Setting up the app requires you having Steam running on your PC so that when you sign into the app on your phone, it can recognize your computer and then you have to enter a four-digit key into your PC. After that, you should be pretty free and clear to play from anywhere that has decent speed.
I tried it out last night and it worked okay. I played some Gato Roboto in the same wifi network as my PC with the virtual on-screen buttons and though there was some lag, service never filly dropped out. The main problem was playing an action/platformer with virtual on-screen buttons. Luckily, the app does allow you to use iPhone compatible controllers. When I was done playing, I turned off my phone and went to sleep, assuming shutting off my phone would close out the app and Steam, etc., but when I looked at my PC this morning, Gato Roboto was still running, so I accidentally logged a good eight hours of play of the titular Gato just waiting around for me to do anything.
My first impressions, in a good wifi network, were positive. I'm excited to try it out with a legitimate controller. I'm one of those weirdos that is very excited about the future of playing high-end PC games on my phone laying in bed.