The PlayStation 4 has been jailbroken via a kernel exploit according to a hacker known as CTurt.
The exploit allows the console to run homebrew software by dumping the RAM from other processes and from there, creating and installing custom firmware. This process would also allow the use of pirated software on the console.
At the moment, the kernel exploit can be used on 1.76 version of the PlayStation 4 firmware but the exploit could be tweaked to work for more recent firmware. There is no easy loading method of using the exploit but is likely that people like CTurt are working on such a system to allow easier access into the console that others can use.
PS4 kernel exploit finally working! Thanks to everyone involved!
— CTurt (@CTurtE) December 6, 2015
PlayStation 4 is currently available now.