In primates, the appearance of an object moving in the peripheral visual field elicits an interceptive saccade that brings the target image onto the foveae. This foveation is then maintained more or less efficiently by slow pursuit eye movements and subsequent catch-up saccades. Sometimes, the tracking is such that the gaze direction looks spatiotemporally locked onto the moving object. Such a spatial synchronism is quite spectacular when one considers that the target-related signals are transmitted to the motor neurons through multiple parallel channels connecting separate neural populations with different conduction speeds and delays. Because of the delays between the changes of retinal activity and the changes of extraocular muscle tension, the maintenance of the target image onto the fovea cannot be driven by the current retinal signals as they correspond to past positions of the target. Yet, the spatiotemporal coincidence observed during pursuit suggests that the oculomotor system is driven by a command estimating continuously the current location of the target, i.e., where it is here and now. This inference is also supported by experimental perturbation studies: when the trajectory of an interceptive saccade is experimentally perturbed, a correction saccade is produced in flight or after a short delay, and brings the gaze next to the location where unperturbed saccades would have landed at about the same time, in the absence of visual feedback. In this chapter, we explain how such correction can be supported by previous visual signals without assuming "predictive" signals encoding future target locations. We also describe the basic neural processes which gradually yield the synchronization of eye movements with the target motion. When the process fails, the gaze is driven by signals related to past locations of the target, not by estimates to its upcoming locations, and a catch-up is made to reinitiate the synchronization.