From the official PlayStation blog

A quick update on backward compatibility – With all of the amazing games in PS4’s catalog, we’ve devoted significant efforts to enable our fans to play their favorites on PS5. We believe that the overwhelming majority of the 4,000+ PS4 titles will be playable on PS5.

The fact that PS5 will not have full backwards compatibility with PS4 games is a disappointment, even though I've seen some people express joy in this update. I'm sure most big games will still run, and that's great, but it feels like they should have done better here.

What's really disappointing is that as far as we know, there is zero PS1, PS2, or PS3 compatibility. With all this power at their disposal, emulating PS1 and PS2 games should be a breeze. The PS3 was notoriously complicated, but PCs are able to do this really well today, so it seems like it should be there too.

Sony has a remarkable collection of games on their 4 major consoles, and it's a shame that it currently looks like you will only be able to enjoy PS4 and 5 games on this new machine. Unleashing that libraary of games on the new console would make this The PlayStation and would help them get the gamers who want the new, as well as those who want to relive the classics. Maybe Sony has a summer announcement where they'll reveal expanded compatibility, but I wouldn't hold my breath.

I should mention that PlayStation Now lets you play some PS2 and PS3 games, but only via streaming and it is only an average experience in my time with it.