Pokémon Colosseum was released in 2003 (Japan) and 2004 (international) for the Nintendo GameCube.
The game contains two modes: Story Mode and Battle Mode. In Story Mode, the player can play through a story set in the Orre region and capture a total of 52 Pokémon (not counting their evolutions). In Battle Mode, the player can engage in several battle challenges, using either Pokémon captured in the Story Mode, or Pokémon from a connected Game Boy Advance game. Two players can use Battle Mode to conduct battles using teams from their Game Boy Advance games, similar to the Stadium games.
This game remains the only way that a player trying to complete the National Dex in any Generation 3 game can obtain Ho-Oh.
Note that all of these pages are basically just Trainer dumps currently, and some pages have very little explanatory text. This is because I don't know much about Colosseum generally. As I play through and put notes together, these pages will be updated to have more of a description.