PS3 Games on PS4: Not Compatible, But Workarounds Exist

No, PS3 games are not compatible with PS4.

Different architectures and operating systems make it impossible for PS4 to run PS3 games natively.

Workarounds:

• PS Now: Sony's streaming service; monthly subscription for PS3 game library on PS4 (and other devices).
• PS4 Pro limited backward compatibility: Small selection of PS3 games playable via this feature.

To play PS3 games, you'll need a PS3 console.