A hacker has purportedly managed to find an exploit in the PlayStation Vita, paving the way for an application which could load homebrew code.
Specifics pertaining to the exploit have yet to be revealed but the hacker, Yifan Lu, did release several lines of code for his project. He's encouraging fellow developers to help him with the application.
Currently, there isn't any homebrew programs available. However, Yifan Lu's Github page states that the new loader is "heavily" based off Half Byte Loader for the PSP, which is an open-source program that enables the ability to run homebrew applications on the Vita's predecessor.