Could a machine think? Could the mind itself be a thinking machine? The computer revolution transformed discussion of these questions, offering our best prospects yet for machines that emulate reasoning, decision-making, problem solving, perception, linguistic comprehension, and other mental processes. Advances in computing raise the prospect that the mind itself is a computational system—a position known as the computational theory of mind (CTM). Computationalists are researchers who endorse CTM, at least as applied to certain important mental processes. CTM played a central role within cognitive science during the 1960s and 1970s. For many years, it enjoyed orthodox status. More recently, it has come under pressure from various rival paradigms. A key task facing computationalists is to explain what one means when one says that the mind “computes”. A second task is to argue that the mind “computes” in the relevant sense. A third task is to elucidate how computational description relates to other common types of description, especially neurophysiological description (which cites neurophysiological properties of the organism’s brain or body) and intentional description (which cites representational properties of mental states).