Humans and other primates are equipped with a foveated visual system. As a consequence, we reorient our fovea to objects and targets in the visual field that are conspicuous or that we consider relevant or worth looking at. These reorientations are achieved by means of saccadic eye movements. Where we saccade to depends on various low-level factors such as a targets’ luminance but also crucially on high-level factors like the expected reward or a targets’ relevance for perception and subsequent behavior. Here, we review recent findings how the control of saccadic eye movements is influenced by higher-level cognitive processes. We first describe the pathways by which cognitive contributions can influence the neural oculomotor circuit. Second, we summarize what saccade parameters reveal about cognitive mechanisms, particularly saccade latencies, saccade kinematics and changes in saccade gain. Finally, we review findings on what renders a saccade target valuable, as reflected in oculomotor behavior. We emphasize that foveal vision of the target after the saccade can constitute an internal reward for the visual system and that this is reflected in oculomotor dynamics that serve to quickly and accurately provide detailed foveal vision of relevant targets in the visual field.