Based upon observations made in the cat, it was proposed that target motion signals are used to predict its future position so as to assure a spatial lead of gaze at saccade end, instead of attempting a precise capture of the target. However, behavioral investigations in macaques do not support this claim. In the non-human primate, primary (interceptive) saccades toward a target moving with a constant speed do not land ahead of the target. They either lag behind the target or they are accurate (Fleuriet et al. 2011), even when the saccade trajectory is unexpectedly perturbed by a brief microstimulation in the superior colliculus (Fleuriet & Goffart 2012). In fact, the landing position of saccades depends upon the target acceleration (Quinet and Goffart 2015). Saccades undershoot the target when it accelerates but overshoot it when it decelerates. Regarding the neurophysiology, interceptive saccades were proposed to be the outcome of the summation of signals ”computed” by two parallel neural pathways. One computation would estimate the location where the target first appeared whereas the other would calculate the subsequent target displacement amplitude from velocity signals. These computations would involve activity propagating through two distinct pathways, a cortico-colliculo-reticular pathway and a cortico-ponto-cerebello-reticular pathway. Thus, the latter stream of activity would be responsible for producing, in a predictive manner, the movement component required to orient gaze toward the future location of the target (”future” relative to the snapshot taken by the former stream). Rather skeptical that kinematic parameters could be embedded within the brain activity, and that massively distributed and recurrent neuronal networks would subtend human-like arithmetic computations, we re-examined this theory. We recorded the activity of saccade-related neurons in the superior colliculus with the aim to test whether the population bursting activity would also include cells coding for saccade vectors corresponding not only to the current location of the target but also to its future locations (Goffart et al. 2017). Thus, we found that during the saccade-related burst, the active assembly does not include cells whose firing codes for saccades toward future locations of the moving target. Instead, it consists of a population of neurons issuing a continuum of commands, ranging from those related to antecedent target locations to commands related to its current location. Regarding the cortico-ponto-cerebello-reticular pathway, we tested its contribution by inactivating one of its output nuclei, the caudal fastigial nucleus (Bourrelly et al. 2018). Like saccades toward a static target, the horizontal component of interceptive saccades became hypometric when directed toward the contralesional side and hypermetric when they were ipsilesional. The horizontal dysmetria depended on target velocity, but the use of accelerating or decelerating targets revealed that velocity was not the crucial parameter. Altogether, our investigations lead to a viewpoint where basic intrinsic properties of the brain suffice to explain the generation of accurate visually-guided (saccadic and pursuit) eye movements without considering that kinematic notions would be embedded within the brain functioning and that the brain would perform arithmetic computations upon them (Goffart et al. 2018; Goffart 2019).