I'm writing this article to try to help clear up a few misconceptions about the current state of PS3 homebrew. This article is intended to be informative and unbiased. Please let me know if there are any problems with it.
Opening up the PS3 has been greatly desired by homebrewers and hackers everywhere. The PS3 is the most powerful video game console on the market today - arguably much more powerful than most computers you could go out and buy for twice the price. I won't dwell on this too much though, it would probably be a good idea to just see the hardware specs for yourself. With the ability to run unsigned (or "homebrew" or "home-made") code on the PS3, we would be able to use many powerful full speed emulators (it would probably even be possible to get Dolphin running decently on the PS3), play many ports of great games, and use lots of original games and software which takes advantage of the unique capabilities of the PS3 (Move anyone?). In short: PS3 homebrew would be awesome.
People have been working on hacking the PS3 to turn it into an open system ever since it was first released. For awhile, people had been using the PS3's OtherOS feature to use Linux to run unsigned code. However, the possibilities through Linux were very limited. Another way to run code was needed. Former hacker George Hotz took the first real steps toward realizing this when he was successful in using Linux to dump important information from the PS3 - the PS3 hypervisor (the software "kernel" which keeps the PS3 security running strong). Xorlorser wrote great plugins and scripts for the "hacker favorite" disassembler IDA Pro so that anyone could easily read the hypervisor in it's PowerPC assembly. Disane (aka Grojcig) recently wrote a great article on reversing the dumps to help people get started too.
Groups of PS3 hackers started to really surface after geohots' exploit. Everyone began looking into the PS3 hypervisor for bugs to help them dump more information or methods to easily execute unsigned code. Yours truly even spent some time doing this and helping people get set-up to do it. Like in any video game console homebrew scene though: Along with people making real progress on PS3 hacking, many people are also just trying to garner public attention for money (via excessive begging and ridiculous promises of course) claiming that they could really open up the PS3 if they got what they wanted. To that end, you should avoid the PS3 "hackers" Mathieulh, DemonHades, and approach most other people claiming they can hack the PS3 for your money with extreme caution. Hackers Xorlorser, Matt_P, phiren, Disane (aka Grojcig), bushing, subdub, AerialX, megazig, and a few others, collectively now called the "psgroove team" are all the real deal as far as people who can actually hack the PS3. Again, use caution if looking at someone asking for something so they can hack the PS3.
However, true PS3 homebrew finally came in an unexpected manner on August 18th, 2010: Ozmodhips revealed that they had in their hands a modchip called psjailbreak which when plugged into a USB port would allow people to run their own unsigned code. As a bonus, the modchip would ship with software enabling users to use make and run "backup" (ie: pirated) copies of games. The modchip also has an SDK freely available to anyone and everyone to write PS3 homebrew.
Several problems arose from the PSJailbreak modchip. 1)The development SDK offered is illegal and is mostly composed of code from SONY's official PS3 SDK. 2)SONY has already filed lawsuits against everyone selling the modchips making it impossible for retailers to ship them until the lawsuits are resolved. This has essentially stopped distribution of the chip. 3)Not necessarily a problem, but the modchip was way overpriced (in my opinion at least) and carries the risk of SONY blocking it in future firmware updates.
Merely days later, phiren and the rest of the "psgroove team" solved all these problems. They reversed the PSJailbreak modchip and released an open source version of it called PSGroove. By flashing PSGroove to a micro controller like one from the AT90USB family you can have a USB stick that does essentially the same thing as the PSJailbreak modchip (without the piracy features though). So finally, after the years of work by hackers, people can run homebrew on their PS3's. A completely legal homebrew SDK for the PS3 is currently under development so we should be seeing lots of PS3 homebrew once it's functional. I've personally got plans (despite not owning a PS3 or one of these USB microcontrollers yet -- donate plz :3 ) to work on a few ports with some people once it's done.
Now the PS3 homebrew "scene" is finally taking off lots of great stuff should be coming soon. Hopefully a software exploit will come about some day so people can more easily run unsigned code; However making a USB PSGroove device is not that bad of an alternative at all - you should check out rvlution.net if you need help.