Yes, it is possible to jailbreak a PS4, provided the console is running a specific, older firmware version, typically 12.52 or lower. Consoles with the latest, updated software cannot be jailbroken with current public methods, as Sony consistently patches the vulnerabilities used in these exploits.
Key Information about PS4 Jailbreaking
Firmware is Crucial: The ability to jailbreak depends entirely on the console's system software version. If your PS4 has been updated to the latest firmware (which requires an internet connection for online play), you likely cannot jailbreak it.
Method: Jailbreaks typically involve using specific software exploits, often loaded via a USB drive or a specially prepared Blu-ray disc. The "jailbreak" is usually temporary (referred to as HEN, or Homebrew ENabler) and must be re-enabled after a full shutdown, though it persists in rest mode.
Risks and Trade-offs:
No Online Gaming: A jailbroken PS4 cannot access the PlayStation Network (PSN), meaning no online multiplayer, game updates, or access to the PlayStation Store. Attempting to go online with a modified console will likely result in a permanent ban of the console.
Warranty Voided: Jailbreaking voids any remaining warranty on the console.
Access to Homebrew and Mods: The main benefit is the ability to install homebrew applications, emulators for older systems (like PS2 and PSP games), mods, and custom themes.
Piracy Concerns: While homebrew and emulation are common uses, jailbreaking is also widely associated with software piracy.