This volume provides an introduction to and review of key contemporary debates concerning connectionism, and the nature of explanation and methodology in cognitive psychology. The first debate centers on the question of whether human cognition is best modeled by classical or by connectionist architectures. The second centres on the question of the compatibility between folk, or commonsense, psychological explanation and explanations based on connectionist models of cognition. Each of the two sections includes a classic reading along with important responses, and concludes with a specially commissioned reply by the main contributor. The editorial introductions provide a comprehensive survey and map through the debates.