The Dark Knight Universe is the reality of Earth-31, a parallel earth. Earth-31 is one of fifty-one divergent realities that branched from the core New Earth reality during the recreation of the Multiverse shortly following the events of Infinite Crisis. This reality is the setting of all of Frank Miller's Batman stories (although Batman: Year One is also considered part of the canonical DC Universe).
Frank Miller's controversial, more ruthless interpretation of Batman begins his crimefighting career after a ten year absence from Gotham City. This Batman considers himself "no killer," but uses particularly brutal methods, leaving criminals with permanent injuries. He also has a taste for casual sexual relationships, having a love affair with Catwoman and whimsically engaging in intercourse with Black Canary. Batman "fires" Dick Grayson from the position of Robin, replacing him with Jason Todd. When Jason dies, Batman retires at 45. After making a comeback at 55, he eventually kills Dick Grayson, who has become a serial murderer under the guise of the Joker. The continuity includes: