fail0verflow, a group known for their work on Wii, PS3 and Wii U(unreleased) exploits, have published a blog entry on their plans for PS4. They have shown a video of a linux boot and running pokemon(ps4 has games now, hell yeah) on the system. They have demonstrated interest in optimizing a linux port for it, and mentioned the name SteamOS. PS4 is considered an insecure system(very opposite to the Vita), fail0verflow are not releasing any exploit themselves which they claim might lead to piracy, but when someone does(they expect someone will), Linux will be sorted out on the system, in hope the main focus of an eventual PS4 jailbreak is not piracy.
https://fail0verflow.com/blog/2015/console-hacking-2015-liner-notes.html