Depending on your PlayStation 3 model, will determine the type of Jailbreak and exploits available to you. The first step of the process checking your console and model number.
Exploit / Jailbreak
Available Console's
Notes
Custom Firmware
Nothing here yet
FAT = Supported
CECH - 20xx / 21xx CECH - 25xx This is the only model that needs a closer look. Some can use CFW and some can not use it. Consoles with a minimum version (minver) of 3.56 or lower can install CFW. Consoles with a minver of 3.60 or higher must use HEN.
An offline tool called MinVerChk (Minimum Version Checker) can also be used to find the minver. It is disguised as a firmware update. When you try to install it, the installation will fail and it will tell you the minver. It is available HERE.
There is an online tool used to jailbreak PS3's. It can also tell you if your PS3 is compatable or not by checking its minver. It will discussed in the jailbreaking guide that is linked below. If the tool tells you that your PS3 is not CFW-compatable, then you must use HEN. (via @coro) CECH - 3xxx
SuperSlim = Not Supported
3.56 Firmware and lower can install a CFW PUP without an exploit. (just install the CFW via USB method)
If on a higher firmware (likely for most) you can update to a firmware that is available for PS3 Toolset (upto 4.92 currently) Does not Require HFW *** Recommended as the safest method, Online method only.
Alternatively, for an offline solution or a solution for 4.93 support the Flash Writer is available Requires HFW ,
>PS3HEN
All PS3 Console's can run PS3HEN
Requires HFW
Not as powerful as CFW but very capable
qCFW
SuperSlim & Slim (NOR Chip)
SuperSlim Models with eMMc chips are not supported.
