Eye movement research is a highly active and productive research field. Here we focus on how the embodied nature of eye movements can act as a window to the brain and the mind. In particular, we discuss how conscious perception depends on the trajectory of fixated locations and consequently address how fixation locations are selected. Specifically, we argue that the selection of fixation points during visual exploration can be understood to a large degree based on retinotopically structured models. Yet, these models largely ignore spatiotemporal structure in eye-movement sequences. Explaining spatiotemporal structure in eye-movement trajectories requires an understanding of spatiotemporal properties of the visual sampling process. With this...