In prepartion for the PlayStation Vita's impending February 22 launch, Sony has released a guide explaining how to download PSP games to the new handheld, along with a list of the 275 games that will be compatible at launch.
If you want to play PSP games on your Vita, you'll have two ways to get them there. The first (and simplest) way is to head to the PlayStation Store over your Vita's Wi-Fi connection and download the games from the download list. Your second option is to transfer the games from your PS3 to the Vita with a USB cable and the handheld's built-in Content Manager.
The list of compatible games is a fairly thorough one, including a 157 PSP titles and 118 PlayStation Minis, but there are certainly some big names that didn't make the list. At the moment, both GTA spinoffs and Metal Gear Solid: Peace Walker are nowhere to be found, but Sony assures us they'll be updating the list in the weeks leading up to launch.
A word of warning, though: you'll only be able to transfer these games over if you've purchased them digitally on your PSN account, as Sony recently announced that they have no plans to bring Japan's UMD passport program stateside.