Are PS3 games playable on the PS4

As someone who never had a ps3, I know I've missed out on good games, and I'm also still on past gen(360) in terms of consoles I own.

So is there a way I can play all the ps3 games I've missed out on and enjoy new gen games on the ps4 Phone Post 3.0

Not directly, although some will be remastered for PS4 and some are available via the Playstation Now streaming service.

Sagiv is correct.

I really wish they had made it backwards compatible. I still play some of my PS3 games so I left both consoles hooked up. The problem for me is that I didnt want to punch holes into my drywall to run another HDMI line from my TV to entertainment center so I went with an HDMI switch. It might just be in my head, but i swear I'm getting some signal degradation going through that switch.

fuck you sony.

No but Xbox one games are. Phone Post 3.0