Concepts are mental representations corresponding roughly to words. Construed as semantic pointers, concepts are capable of playing inferential roles, but they also maintain embodied connections with sensory–motor processes. Understanding concepts in this way enables us to give biologically and psychologically plausible accounts of innateness, learning, and categorization. Learning new concepts can occur not only through slow, incremental use of multiple examples but also by fast, sometimes revolutionary conceptual combinations. The process of categorization is carried out by retrieval through reactivation of neural patterns and through parallel constraint satisfaction accomplished by competition among semantic pointers. Categorization can contribute to different kinds of problem solving, including planning, decision making, and explanation. Concepts do not have strict definitions, but they can nevertheless be meaningful because of their relations with sensory and motor inputs and with other concepts.