Every new console generation brings up questions about backward compatibility with previous, and sometimes more well-loved, games. Tough nothing official has been disclosed, sources close to the matter have revealed that the latest PlayStation 4 will practically support titles from the PlayStation 1 and PlayStation 2 via hardware emulation.
It might surprise some to know that Sony has actually had a history of supporting older games, though that history hasn't exactly been consistent nor desirable. In particular, the PlayStation 3 firmware actually supported hardware emulation for PS1 and PS2 as well as PSP. The PS Vita, on the other, used the same technology for running PS1 games as well.
Unfortunately, Sony has phased out hardware emulation and transitioned over to software emulation, in cases where it didn't actually scrap support for playing older games. The PlayStation 4 has already been reported to soon play PlayStation 3 games, but that will be through the newly unveiled PlayStation Now streaming service.
Sony surprisingly won't be taking the same route for PS1 and PS2 games. Instead, those titles will run locally via hardware emulation once again. There is even talk that Sony is pushing for native HD resolutions without having to go through the process of remastering those games. As mentioned previously, Sony already has the technology and the experience to execute this.
Of course, nothing is official yet. Sony can also very well end up using PlayStation Now to stream all previous gen titles, which might be a better business move to promote its streaming service. There will definitely be benefits to running things locally even via emulation, like less input latency and better HD scaling, but any game that can run on the PS3 can also run on PlayStation Now as well. Sony might try to take the path of least resistance in terms of technology and distribution, but we hope they will make the best decision for gamers.