Xbox 360

Console hacks
This details "full" hacks, the end result of whichis to run a custom dashboard, either Freestyle Dash, or the in-progress Aurora. FSD is tried and tested, but no longer in active development, while Aurora is actively going and shows promise. Either of these allows you to do do virtually anything with you 360, running retail games from internal and external HDD, pirating XBL content including DLC, running homebrews, even Linux if you're so inclined. Features like integrated FTP server make it easy to manage contents on your console once you're set up.

The downside to these hacks is that you can't connect to live - if you do, your console will be banned almost instantly. It is possible to play online with other people also using a hacked console, using XLink Kai, but as this works as a VPN like Hamachi, it limits you to LAN play.

These hacks are differentiated from drive mods and Optical Drive Emulators, which pretty much end at running pirates retail games, but CAN go online (with some precautions) and are talked about below.

Reset Glitch Hack
The most recent hack for the 360, and the most comprehensive, being compatible with every model (except the most recent, the Winchester motherboard in the 360 E model) and every dashboard version released so far. The oldest revision, the Xenon, is technically compatible, but takes several hours to boot each time so is only useful for recovery of a lost DVD key.

Unlike most other console hacks of this generation and before, this is quite an involved process, and requires you to buy some proprietary hardware, and to have soldering equipment and technique. Alternatively, you could find someone who is willing to have your console shipped to them and install the mod for you, for a fee. Team-Xecuter's modding services subforum is a good place to find reputable people for this.

If you want to do it yourself, the most complete tutorial (that I could find at the time of writing this) is here http://www.se7ensins.com/forums/threads/jtag-rgh-r-jtag-xbox-360-ultimate-exploit-guide.804054/ This will walk you through al the way to getting Freestyle launching

It is slightly out of date, as the sections covering the CR3/R-JTAG have been supplanted by the release of the CR4XL, for which you can find install guides here http://team-xecuter.com/forums/forumdisplay.php?252-Xecuter-CR4-XL-Support

JTAG Hack
The JTAG hack is the precursor to the RGH, and achieves the same end with a simpler method. Unfortunately it was fixed shortly after release, if your console is running dash 2.0.8498.0 or higher, it won't work. If you do still have a 360 left unupdated after all these years, however, setup is detailed in the se7ensins link above.

King Kong Exploit
The first hack of its kind for the 360, used a copy of the game King Kong to exploit the hypervisor. Patched with dash 2.0.4552.0, and since the JTAG hack there's no reason to use this any more. http://beta.ivc.no/wiki/index.php/Xbox_360_King_Kong_Shader_Exploit does have instructions for setup, if you really need your convoluted gentoo fiDE

The very first hacks for the 360 were for flashing the DVD drive to play burnt discs. Getting this working does also require some extra hardware, how much and how complicated the process is again depends on which revision you have.

The general idea is to extract your DVD drive's unique key, and use that to create and flash a custom firmware to the drive. For some drives, further hardware is required, for some it's as simple s a cheap probe, but for most slim models and onward you need to buy a replacement PCB for the drive. The Jungleflasher PDF covers just about every model available.

If you plan to go online, you'll also want to research using abgx360, and stealth patching your disc images before burning them. https://gbatemp.net/threads/stealth-patching-with-abgx360.347771/

Also note that almost all games published after the release of Halo Reach use XGD3 protection for their discs, which most regular DVD writers can't bypass. You'll need to have or obtain a compatible DVD drive and use this custom payload injector for them to work.

Optical Drive Emulators (wip)
These achieve a similar result to drive hacks, but rather than burning and using discs, you use game files stored on a hard drive, connected to the ODE, which connects to your console via the DVD drive. You still need to obtain your DVD drive key, but thecess is easier. Some resellers for ODEs offer an installation service, which saves you having to buy any further single-use hardware.