Nintendo DSi
The Nintendo DSi was release on November 1, 2008 in Japan, and April 5, 2009 in North America. It was the third revision of the Nintendo DS line of handhelds, and features new additions over the prior two consoles.
The DSi featured a new design to the Lite, with a matte finish, outward- and inward-facing cameras, and a new charging port not compatible with any prior DS (though it was later used for all 3DS models). Notably, the DSi removed the Gameboy Advance slot (officially referred to as "Slot-2") and thus makes it incompatible with any game requiring the GBA slot. Nintendo added a greater range of WiFi support, with new security compatibility and more connection slots. Only games designed to take advantage of the DSi Internet settings are compatible, meaning most DS games still required a lower-end security connection to function.
Nintendo DSi XL
The DSi itself recieved a revision in the form of the DSi XL ("DSi LL" in Japan). This model featured a glossy top lid, large wide-viewing-angle LCD screens that maintained the resolution of the DSi, additional hinge settings, and improved battery life. The DSi XL was released on November 21, 2009 in Japan, and March 28, 2010 in North America. The Nintendo 3DS was announced five days prior, on March 23, at E3 2010.
Homebrew
Due to it's new SD card slot, the DSi became a prime target for Custom Firmware (or "CFW") and other forms of homebrew. The best guide to DSi hacking is the DSi Hacks Guide, which helps you install the frontend TWiLight Menu++ as well as other setup steps. This allows you to do things such as run dumps of DS games, emulate numerous consoles, play a wider selection of media than is built-in with the system, and set up custom behaviors like default launch programs, startup hotkeys, and more.
The DSi featured updatable firmware akin to the Nintendo Wii, and as such, Nintendo took every opportunity to patch out flash cards in an effort to fight piracy of their games. Some flash cards work on DSi, as they were continuously updated after official Nintendo firmware support ended, however this is less effective and less featured as a fully homebrewed DSi.
Trivia
You can raise or lower the screen brightness of the DSi at any time, without the need to enter System Settings, by simply holding the SELECT button and then pressing + or - volume.