The ability of smooth pursuit eye movements to anticipate the future motion of targets has been known since the pioneering work of Dodge, Travis, and Fox (1930) and Westheimer (1954). This article reviews aspects of anticipatory smooth eye movements, focusing on the roles of the different internal or external cues that initiate anticipatory pursuit.We present new results showing that the anticipatory smooth eye movements evoked by different cues differ substantially, even when the cues are equivalent in the information conveyed about the direction of future target motion. Cues that convey an easily interpretable visualization of the motion path produce faster anticipatory smooth eye movements than the other cues tested, including symbols associated arbitrarily with the path, and the same target motion tested repeatedly over a block of trials. The differences among the cues may be understood within a common predictive framework in which the cues differ in the level of subjective certainty they provide about the future path. Pursuit may be driven by a combined signal in which immediate sensory motion, and the predictions about future motion generated by sets of cues, are weighted according to their respective levels of certainty. Anticipatory smooth eye movements, an overt indicator of expectations and predictions, may not be operating in isolation, but may be part of a global process in which the brain analyzes available cues, formulates predictions, and uses them to control perceptual, motor, and cognitive processes.