To clearly see a moving object, an observer must rotate his or her eyes with a velocity that matches that of the object. Such rotations are called smooth pursuit eye movements, and they depend critically on the ability of the primate brain to integrate information about object velocity from various local motion signals. When the local motion signals are in conflict, it is possible to use smooth pursuit eye movements as a continuous read-out of the motion integration process. This review discusses the results of recent behavioral experiments that have taken this approach, along with relevant neurophysiological and computational studies.