Ocular pursuit movements allow moving objects to be tracked with a combination of smooth movements and saccades. The principal objective is to maintain smooth eye velocity close to object velocity, thus minimising retinal image motion and maintaining acuity. Saccadic movements serve to realign the image if it falls outside the fovea, the area of highest acuity. Pursuit movements are often portrayed as voluntary but their basis lies in processes that sense retinal motion and can induce eye movements without active participation. The factor distinguishing pursuit from such reflexive movements is the ability to select and track a single object when presented with multiple stimuli. The selective process requires attention, which appears to raise the gain for the selected object and/or suppress that associated with other stimuli, the resulting competition often reducing pursuit velocity. Although pursuit is essentially a feedback process, delays in motion processing create problems of stability and speed of response. This is countered by predictive processes, probably operating through internal efference copy (extra-retinal) mechanisms using short-term memory to store velocity and timing information from prior stimulation. In response to constant velocity motion, the initial response is visually driven, but extra-retinal mechanisms rapidly take over and sustain pursuit. The same extra-retinal mechanisms may also be responsible for generating anticipatory smooth pursuit movements when past experience creates expectancy of impending object motion. Similar, but more complex, processes appear to operate during periodic pursuit, where partial trajectory information is stored and released in anticipation of expected future motion, thus minimising phase errors associated with motion processing delays.