Recent experimental research in the field of neurophysiology has led to the discovery of two classes of visuomotor neurons: canonical neurons and mirror neurons. In light of these studies, we propose here an overview of two classical themes in the cognitive science panorama: James Gibson's theory of affordances and Eleanor Rosch's principles of categorization. We discuss how theoretical perspectives and neuroscientific evidence are converging towards the current paradigm of embodied cognition. From this perspective, we discuss the role of action and simulation in cognitive processes, which lead to the perceptual recognition of objects, and actions and to their conceptual categorization.