Shadow Pokémon are a concept exclusive to Pokémon Colosseum and Pokémon XD. Shadow Pokémon have been corrupted by the villainous group Cipher. Shadow Pokémon do not have access to any of their expected moves; instead, they can only use the Shadow Pokémon-specific move Shadow Rush. Shadow Pokémon cannot be traded out of the game, be given nicknames, or evolve. A Shadow Pokémon does not gain experience as normal; instead, as you battle with a Shadow Pokémon, its Heart Gauge begins to empty, a process called Purification.
Once a Pokemon's Heart Gauge has been reduced to zero, it can be taken to the Relic Stone in Agate Village, where the Shadow Pokémon status can be fully removed. Once this occurs, a Pokémon will immediately gain all the experience it would have obtained up to this point were it not a Shadow Pokémon. It will lose access to Shadow Rush and gain the moveset a normal Pokémon of its species would have. All Purified Pokémon receive the National Ribbon at this time.
There is a single-use item called a Time Flute that, when used in Agate Village fully Purifies a Shadow Pokémon instantaneously. However, there are only two Time Flutes in the game. One is given to you by Vander after completing the Mt. Battle section of the game. The other is located in an area in Pyrite Town only accessible through The Under.
Exactly 50 Shadow Pokémon exist within the game. A list is available.
In Pokémon Colosseum, there are no wild Pokémon to capture in the usual fashion. Poké Balls, a rarity in Orre, are only used in this game to snag Shadow Pokémon. Snagging a Shadow Pokémon works just like catching a regular Pokémon, except that you are capturing (snagging) the Pokémon from another Trainer during a Trainer battle.