There exist numerous explanations for the phenomenon of multistable perceptions (e.g., ambiguous figures or binocular rivalry). Some of the explanations see the answer very early in the visual system as a competition between the monocular retinal inputs. Others like Helmholtz or James, for example, considered attentional mechanisms on higher cognitive levels to be relevant for these phenomena. This article, which is based on a talk presented at the Parmenides faculty meeting 2007, describes and summarizes the main results obtained by electrode measurements of single-cell and open-field activities in different areas of the visual system starting from V1 and V2 in the striate and early extrastriate cortex over V4 and MT up to the inferior temporal cortex. We compare single-cell activities with the reports of the mental perceptions of trained monkeys. The correlations between cell activity and perception increase significantly towards the higher cognitive areas, but are already present within the striate cortex. Our findings suggest that there is no single mechanism for the suppression of visual input but that a series of processes of neural mechanisms at different levels of the visual hierarchy contribute to the overall effect. Even though the article does not address the issue of thinking explicitly, a deeper understanding of how perception is processed in the brain and, in particular, how the correlates of certain neural activities get into the focus of attention and become conscious seems to me a necessary prerequisite for understanding thinking.