Comic Book History
When Two-Face was first introduced in the Batman comics, his name was Harvey Kent. This was changed so people wouldn't be confuse it for Clark Kent, the alter-ego of Superman. After having the left side of his face horrifically disfigured by acid thrown in his face, Dent lost his mind and gave into the rage which had quietly been building within him for years. Dent suffers from a curious case of multiple personality disorders in which the two personalities - the noble "Harvey" and the monstrous "Two-Face" - are blended together into one gestalt mind that is incapable of making its own decisions. Instead, Two-Face relies on pure luck to make choices for him, in the form of a two-headed coin owned by Harvey Dent, which he scarred one side of. If the coin comes up on the clean side, he does the right and noble thing, while if the scarred side comes up, he does something cruel and monstrous.
Back in the silver age, when comic books were silly and light-hearted, Two-Face used to have gimmicky plots where the number 2 was involved in all of his crimes, like robbing the Second National Bank on 2nd street at two o'clock. He has made many appearances in movies and video games. He is one of Batman's deadliest foes, and because he relies entirely on luck, he is wildly unpredictable.
Batman: Arkham City
With The Joker presumably weakened and healing from his overdose of Titan, Two-Face goes to war with the Clown Prince of Crime and The Penguin for control of Arkham City. However, after his failed attempt to "try" Catwoman in court (which is foiled by Batman), he disappears until the final Catwoman segment of the game, or altogether for those without the Catwoman content. Two-Face is voiced by Troy Baker.