Two-Face, real name Harvey Dent, was a mentally unstable former District Attorney who had an obsession with the concept of dualism, and was a common rogue of Batman.
History[]
The Dark Knight Returns[]
After Superheroes were made illegal in 1976, Two-Face was put into Arkham Asylum, where Dr. Wolper did an experimental form of psychotherapy and surgery to restore him back to his Harvey Dent persona. It seemed to work. However, he then disappeared afterwards. It eventually was revealed that Wolper's actions actually backfired, as while he did restore Harvey's original face, his psychotherapy if anything worsened Dent's deteriorated mental state and caused him to permanently adopt his Two-Face persona. This resulted in his wearing a mask composed of bandages over his face.
Around the time Batman re-emerged, he had two teams of robbers rob the local bank, and had the teams leave in two separate directions when the police arrived. Eventually, he and his men stole two helicopters, one decommissioned chopper, and one state of the art prototype, and used them to try and hold the Gotham Twin Towers for ransom for $2 million. However, unbeknownst to him, one of his henchmen, Abner, had been a double agent for the Joker (who had emerged from his catatonia thanks to Batman's publicized return in Gotham) and sabotaged the bombs he planned to use as part of his ransom demands to prematurely detonate and kill him and his gang. Batman ultimately saved him by tackling him out of the state of the art chopper and into one of the buildings. Batman upon removing the mask then realized the truth of what happened to him, with Two-Face ruefully admitting that "at least the two sides matched", with Batman sympathizing due to both being forced out of retirement.
In Other Media[]
Batman: The Dark Knight Returns Part 1[]
Two-Face only appears in the first part, where he was one of the major antagonists of the film alongside the Mutant King. Largely because Two-Face's portion of the plot occurred well before Joker emerged from his catatonia, his angst was increased to have him deliberately sabotage the bombs and even lie to his own men because he secretly wanted to commit suicide over his failure to stop being Two-Face.