I introduce the special issue by: (1) outlining something of the relationship between mainstream cognitive science and the study of nonhuman primate cognition; (2) providing a brief overview of the scientific study of primate cognition and how the papers of this special issue fit into that scientific paradigm; and (3) explicating my own views about the relationship between nonhuman primate cognition and human cognition. © 2000 Cognitive Science Society, Inc.