"If I'm going to have a past, I prefer it to be multiple choice". Although there have been a number of occasions in which Joker's past has been "explained", they contradict each other, so it's uncertain as to which - if any of them - are true. It's what makes Joker so interesting and mysterious - perhaps even he doesn't know. One thing we do know, however, is that his face is scarred in to a permanent smile. Did he do it himself in an attempt to make his scarred wife feel better about herself? Did his father do it in a drunken attack? Did Batman do it? Who knows? But the permanent smile he has been left with sure is creepy. Joker is Batman's arch-nemesis and the clown prince of Gotham - a chaotic preparatory genius and complete and utter psychopath whose appearance is a complete juxtaposition to the Dark Knight's moody look.
