Both Batman and Robin were struck by sudden tragedy (they both lost their parents due to criminal elements) which resulted in their mutual vow to fight crime for the rest of their lives. They do so mainly in Gotham City where they live fairly anonymous lives as playboy Bruce Wayne and ward Dick Grayson, but when they are on the job they are disguised.
Being a billionaire Wayne has unlimited funds at his disposal which means that he has a cave filled with useful gadgets as well as a special Batmobile, a Batboat, and a Batplane to aid the two masked do-gooders in their crime-fighting.
Some of the antagonists are recurrent and colourful characters in the stories; Penguin, The Riddler, and The Joker are examples.

Batman (named Bat-Man in the start) is also a member of Justice League of America.