The newest firmware currently is 3.90 M33. Here's what's been going on since 3.40 OE-A, in chronological order...
- 3.50 released
- Dark_AleX leaves the scene
- 3.51 released
- 3.51 M33 released - who is this mysterious Russian M33 group?
- 3.52 and 3.52 M33 released
- Pandora's Battery released - now almost all bricks can be fixed!
- 3.60 released - it's only for Slims, but there's soon an M33 release
- 3.71 M33 released - M33 reveals that it's actually Dark_AleX in disguise. World slaps forehead. 3.71 M33 is compatible with the PSP Slim and PSP Phat, but the 1.50 kernel addon (which lets people play homebrew games which work on 1.50) is only for Phats.
- Despertar Cementario v3 (aka Universal Unbricker v3) released. Now the Pandora can be used to unbrick/downgrade/upgrade all PSPs, Phat or Slim, to 3.71 M33!
- After a long delay, 3.80 M33 is released. Now people can upgrade their custom firmwares via Network Update!
- 3.90 M33 released, only a few days after 3.90.
- Dark_AleX's Time Machine revealed. PSP Slims can now run any firmware, but Time Machine itself is not out yet.
That's the juicy bits, as far as I can remember. Now, how to get to 3.90 M33? It's a long journey...
You have to go to 3.52 M33-4, then 3.90 M33, then you have to install the 1.50 kernel addon if you want to run your old homebrew on it. The 1.50 kernel addon takes away the Korean fonts and LocationFree player, BTW, but 3.40 OE-A takes away those too, so you shouldn't worry.