A substantial body of indirect evidence suggests that some asteroids have satellites, although none has been detected unambiguously. Collisions between asteroids provide physically plausible mechanisms for the production of binaries, but these operate with low probability; only a small minority of asteroids are likely to have satellites. The abundance of binary asteorids can constrain the collisional history of the entire belt population. The allowed angular momentum of binaries and their rate of tidal evolution limit separations to no more than a few tens of the primary's radii. Their expected properties are consistent with failure to detect them by current imaging techniques.