You can play PS3 games on your PS4 with Sony's PlayStation Now streaming service — here's how

You can play PS3 and PS2 games on your PS4 or PC by signing up for PlayStation Now, Sony's game streaming service.

'Do PS4 controllers work on PS3?': How to connect your PS4 controller to a PS3 in 2 ways

PS4 controllers will work with a PS3 console, and when you use a wired connection, there is no setup involved. Here's what ...
Ars Technica

What's involved in porting a game from, say, a PS3 to PS4?

When I bought my PS3 many moons ago I had 2 games on my PS2 I wanted to migrate. Due to a lack of HDMI ports both games got tossed into the PS-2 box, later donated to the library (with a nice tax ...