Shadow Pokemon were mostly in the Colosseum and XD games, but Shadow Mewtwo now exists within the Pokken games. Shadow Pokemon were Pokemon with their hearts closed artificially by an evil organization known as "Cipher". Shadow Pokemon will have shadow moves, which have no strengths or weaknesses.
In the XD and Colosseum games, you have to snag these Pokemon to purify them. In Pokemon Go, you can catch Shadow Pokemon after beating a team GO Rocket Grunt.
That being said, what did you think of Shadow Pokemon? Would you like to see them appear in a main series game?