Linux is a UNIX-like kernel that was created in 1991 by Linus Torvalds. Originally written for the i386 family of computers, it has been ported to many other architectures as well. It is available as free software and forms an essential part of the GNU/Linux operating system, which is often referred to as "Linux" by mistake. Many distributions of GNU/Linux are available which allow users to easily install a GNU/Linux system from pre-built binaries, rather than compile it all themselves.
A fork of the kernel, Linux, was published by fail0verflow on January 3rd 2016, adding support for the PS4. They have also announced working 3D support for the GPU and showed a demonstration through X.Org. As of April 2016, it became possible to run/install GNU/Linux distributions using an exploit with PS4 System Software version 1.76 and a custom kernel.
The PS4 relies on proprietary microcode for the CPU and GPU, so the hardware may not safe to use freedom wise. In addition, the whole process depends on utilizing Sony's non-free firmware and no free firmware replacement exists yet.