PPSSPP allows you to run your PSP games in full HD resolution on your computer and also lets you play them on Android. It can even upscale textures that are too blurry because they were created for the small screen of the original PSP.
You can often run at twice the original resolution on modern Android phones or tablets.
PPSSPP is an open source project licensed under the GPL 2.0 or later. Anybody is welcome to make improvements to the code. PPSSPP's compatibility has been steadily improving, partly thanks to these contributions. This allows us all to play our PSP games on any device we choose.