Imitation requires the imitator to solve the correspondence problem--to translate visual information from modelled action into matching motor output. It has been widely accepted for some 30 years that the correspondence problem is solved by a specialized, innate cognitive mechanism. This is the conclusion of a poverty of the stimulus argument, realized in the active intermodal matching model of imitation, which assumes that human neonates can imitate a range of body movements. An alternative, wealth of the stimulus argument, embodied in the associative sequence learning model of imitation, proposes that the correspondence problem is solved by sensorimotor learning, and that the experience necessary for this kind of learning is provided by the sociocultural environment during human development. In a detailed and wide-ranging review of research on imitation and imitation-relevant behaviour in infancy and beyond, we find substantially more evidence in favour of the wealth argument than of the poverty argument. (Contains 2 footnotes, 1 table and 1 figure.)