People's eyes are directed at objects of interest with the aim of acquiring visual information. However, processing this information is constrained in capacity, requiring task-driven and salience-driven attentional mechanisms to select few among the many available objects. A wealth of behavioural and neurophysiological evidence has demonstrated that visual selection and motor selection of saccade targets rely on shared mechanisms. This coupling supports the premotor theory of visual attention put forth more than 30 years ago, postulating visual selection as a necessary stage in motor selection. We examine to which extent the coupling of visual and motor selection observed with saccades is replicated during ocular tracking. Ocular tracking combines catch-up saccades and smooth pursuit to foveate a moving object. We find evidence that ocular tracking requires visual selection of the speed and direction of the moving target, but the position of the motion signal may not coincide with the position of the pursuit target. Further, visual and motor selection can be spatially decoupled when pursuit is initiated (open-loop pursuit). We propose that a main function of coupled visual and motor selection is to serve the coordination of catch-up saccades and pursuit eye movements. A simple race-to-threshold model is proposed to explain the variable coupling of visual selection during pursuit, catch-up and regular saccades, while generating testable predictions. We discuss pending issues, such as disentangling visual selection from pre-attentive visual processing and response selection, and the pinpointing of visual selection mechanisms, which have begun to be addressed in the neurophysiological literature.