This chapter reviews the two main current approaches to cognitive architecture: rule-based systems and connectionism. Both kinds of architecture assume the central hypothesis of cognitive science that thinking consists of the application of computational procedures to mental representations, but they propose very different kinds of representations and procedures. Both rule-based and connectionist architectures have had many successes in explaining important psychological phenomena concerning problem solving, learning, language use, and other kinds of thinking. Given their large and only partially overlapping range of explanatory applications, it seems unlikely that either of the two approaches to cognitive architecture will come to dominate cognitive science. The chapter suggests a reconciliation of the two approaches by means of theoretical neuroscience. Unified understanding of how the brain can perform both serial problem solving using rules and parallel constraint satisfaction using distributed representations will be a major triumph of cognitive science.