PlayStation 4

Software
There is a released kernel exploit for 1.76 firmware. Booting into Linux is now achievable for the average user. Not all of the PS4's hardware is supported yet, but it is being worked on. It's also possible to call the Package Installer on pre-2.00 firmwares, letting you install DRM free .pkg files. There are also some debug settings available on retail consoles. However, not all are available to the public yet. There's also an FTP Server that's now available, but be careful, since you could brick your PS4.

Hardware
It is possible to duplicate a PS4 console's content by activating an account on it, dumping its NAND and hard drive contents, deactivating the console then rewriting the NAND and hard drive contents back. This does not enable homebrew or unsigned code execution in any way, it only benefits pirates. Source: wololo