This paper describes a framework for researching the Cognition Hypothesis which claims that pedagogic tasks be sequenced for learners on the basis of increases in their cognitive complexity. It distinguishes dimensions of complexity which increase the conceptual and linguistic demands tasks make on communication, so creating the conditions for L2 development, from dimensions which increase demands made on accessing a current interlanguage repertoire during real-time performance. Studies providing some support for three predictions of the Cognition Hypothesis (Robinson 2001a) are then reviewed. Increasing the cognitive demands of tasks along developmental dimensions; a) encourages grammaticization, and so greater accuracy and complexity of L2 production; b) promotes interaction and heightened attention to form, and memory for input, therefore increasing incorporation of forms made salient in the input; and c) individual differences contributing to perceptions of task difficulty progressively differentiate performance and learning as tasks increase in complexity. (Contains 2 figures, 4 tables and 5 notes.)