PPSSPP can run your PSP games on your PC in full HD resolution, and play them on Android too. It can even upscale textures that would otherwise be too blurry as they were made for the small screen of the original PSP.
Here's changelog for 0.9.8 release:
+ OpenGL ES 3 detection bug on Xperia devices fixed, graphics work again.
+ More accurate audio mixing and emulation
+ Software rendering and display list performance improvements
+ Workaround for timing issue hanging Crash Tag Team Racing
+ Galician language
+ Built-in ARM disassembler improvements (dev feature)
+ Fix for immersive mode volume key issue on Android Kitkat
+ And more minor tweaks and fixes as always.
Visit Official homepage for for further information and latest build of emulator