In the latest firmware update for the PS3, Sony has quietly added wireless support for the DualShock4. However, everything is not puppies and rainbows.
The DualShock4 has always worked with PS3 systems through a wired connection, but the cable supplied for the PS4's gamepad is very, very short. The latest firmware update for PS3 allows the console to recognize the bigger brother of the DualShock3 as a generic control pad, which considerably limits it's capabilities. It is, of course, still incredibly comfortable.
While the next-gen controller is now compatible with the last-gen installment of Sony consoles, it does not have all of it's bells and whistles intact. The touch pad, rumble, and sixaxis capabilities for the controller are not accessible while it is synced to your PS3. While wireless gaming is now possible with a DS4, don't expect it to be as fulfilling or immersive as it would be with DS3.
Once synced, the DualShock4 will be recognized by your PS3 as a default controller - meaning that you can turn on your system by pressing the PS button on your DS4. You can, of course, still connect the next-gen gamepad to your next-gen PlayStation. As is to be expected, you can only be synced to one console at a time and you have to unsync from either console if you wish to connect to the other.
If you use your last-gen PlayStation as a Netlfix-box, this update is a gift from the gods. If you use your PS3 as a games console, however, this update is a gold-dipped carrot on a string dangling in front of your nose - but at least you can try to reach that carrot from any part of your living room.