As of 2014, the PS4 console cannot play disc-based PS3 games. Neither the PS4 nor the Xbox One is backward compatible. Sony has recently launched a service that is called PlayStation Now, which is a service that allows some PS3 games to be played on the PS4.
The PlayStation Now is a streaming video game service that is available on the PS4. This service allows gamers to rent digital versions of PS3, PS2 and original PlayStation games for a period of time. They are then able to play the games on the PS4 without having to acquire the original discs.