All PS3s are capable of playing PS1 games, whether they are on disc or downloaded from the PSN.

Only the earlier fat PS3 models can play PS2 disc-based games.

Recently though, Sony have begun adding "PS2 classics" to the PSN store, which are playable on all PS3s. They appear to be using a full software emulation to play these games.

Presumably they have been tweaking the emulator on a per-game basis to ensure that each game runs correctly. (The partial software emulation on the CECHCxx and CECHExx PS3 models was decent, but many games had small glitches.) There is only a very small selection of PS2 games available on PSN at the moment.

All PS3s are capable of playing PS1 games, whether they are on disc or downloaded from the PSN.

Only some earlier fat PS3 models can play PS2 disc-based games.

Recently though, Sony have begun adding "PS2 classics" to the PSN store, which are playable on all PS3s. They appear to be using a full software emulation to play these games.

Presumably they have been tweaking the emulator on a per-game basis to ensure that each game runs correctly. (The partial software emulation on the CECHCxx and CECHExx PS3 models was decent, but many games had small glitches.) There is only a very small selection of PS2 games available on PSN at the moment.