Bruce Wayne was the wealthy son of Thomas and Martha Wayne. Bruce's parents were killed in front of him by who he would later find out was the Joker. Afterwards, Bruce takes on the persona of Batman and swears vengeance as he fights crime.
In Batman Returns, Batman takes on The Penguin and meets Catwoman as both Bruce and Batman.
Vicki Vale: [distracting Joker] Mr. Joker, you make such beautiful things... oh, you're so powerful, and... PURPLE! Oh, I love purple. Batman: Excuse me. [Joker looks] Batman: Have you ever danced with the devil by the pale moon light? [punches him]