By way of emulation.
According to a source within Sony, with the coming of their prized winning entry in the next generation console race, they have finally decided to implement a feature which was slightly addressed with the PS3, but on the whole represents one of the biggest complaints that gamers have had with Sony in recent years: Full on backwards compatibility. That’s right, the PS4 will have backwards compatibility with PS1 and PS2 games by way of emulation. PS3 games will be compatible via cloud services of PlayStation Now.
Sony had made an attempt to phase out the emulation method of playing older games with the PlayStation 3, but now it seems as though they’ve changed their minds. Why? Because local emulation provides a faster, smoother, and graphically superior experience than a streamed game.
This switch in technology also suggests that Sony is making an effort to, not only provide gamers with some nostalgic glory, but also to enhance the experience as much as is reasonably possible given the relatively outdated graphics and gameplay.