What I did not realize was that I can do that over the internet! I was listening to the Official Playstation Blogcast and Justin mentions streaming over the internet in this episode (skip to 1:20:10 to hear him speak about it). I just tested it by tethering my PS Vita to my iPhone 6 Plus (thanks T-Mobile for giving me 3GB of free tethering) and playing Drive Club running on my PS4 at home on my home network.
T-Mobile has some serious bandwidth to use (I sometimes clock it in at 30-50MBps), tonight I was getting around 8MBps and I was playing Drive Club with no noticeable lag over an LTE connection. It was fantastic and as Justin says... Magical.
If you have a PS4 and a PS Vita, give it a shot. If you have a PS4 and don't have a PS Vita, you should seriously think about getting a PS Vita. Follow these handy instructions to get things setup. Then leave your PS4 in Rest Mode so that it can be woken up remotely. You can play PS4 games wherever you may be (all you need is a WiFi connection). This adds even more value to my PS Vita.