Like the Gamecube one, various way to play imports on your ps2.
Method One: Swap Magic
Similar to the Freeloader for the gamecube, the swap magic is a set of two discs (one cd and one dvd) that will allow you to play imports and backed up games. It requires the use of some sort of swap method, whether it be through the knife trick, or installing a no-solder chip in your ps2.
Pros: Very easy to use if you are using no-solder modchip. Minimal modification needed to console(you dont even have to fully take it apart)
Cons: If using knife trick, the process can be tricky, and an inforrect knife swap can damage the tray mechanism in your ps2.
Method Two: HDLoader
HDloader is an application that allows you to run games from the HDD of the ps2. It supports the official HDD that comes with FFXI, as well as any third party hard drive. (the sony HDD is actually a rebadged maxtor). Supports HD sizes up to 2tb (through the use of patches) and compatibility is being worked on constantly (through third party individuals).
Pros: No modification needed to your console. You can either bu the HDloader on disc or find the ELF file and run it through your ps2 memory card using the PSOne exploit.
Cons: COmpatibility is not perfect. Some games refuse to run from the HDD. Messing with compatibility settings can be a chore for some.
Method Three: Modchip
There are various modchips available for the ps2, and just about all of them bypass the region protection of your console. The only direct solution for playing your imports.
Pros: Direct playing of your imports. No messing with exploits, swap discs or anything like that. Just put in your game and play.
Cons: Installing a PS2 modchip can be a very daunting task for those not good with a soldering iron. Even those who are fairly good can easily ruin a ps2 by a solder short. PS2 chips are by far the most difficult chip to install out of the three consoles, usually taking 14-23 wires for install.