Since the release of the PS Vita the privilege to play PS1 games hasn't been managed by Sony themselves (even though they are supposedly working on it). Although Wololo releasing his VHBL can run homebrew and other games to some extent. News has arisen that an anonymous developer using the kernel exploit of the PSP has in fact managed to get PS1 games running. Keep in mind though that this is still in an early phase and no sound can be emulated yet, but the anonymous dev who is going to make this possible is hard at work trying to fix this issue before a full release is made. A video to display the feat of the progress in action can be viewed below. A quote from the source
