The left fielder squints at the baseball as it curves toward him.  He adjusts his hand and body, and the ball lands in his mitt.  Somehow, the changing pattern of light on his retina was transformed into a motor command which  brought his hand to the correct location for catching the ball.  How was this accomplished?  Is there a map of visual space in the brain which encodes the location of the ball and the fielder's glove?  In this article, we review some recent experiments using monkeys, on visuo-motor transformations in the brain.  We ask how neurons represent the location of a stimulus for the purposes of looking at it, reaching toward it, or avoiding it.