Increasingly, economists concur that innovation processes are far from equilibrium phenomena. Indeed, these processes are characterized by complex qualitative changes in the relations between producers, sellers and users, from which new products and new markets emerge. In order to understand such processes, many economists have begun to draw on ideas and methods from 'the sciences of complex systems' literature. In this paper, I examine in detail three concepts from this literature, and I show how, taken together, these concepts provide a foundation for a complexity theory of innovation. I briefly characterize these concepts as follows: (1) The 'more is different' principle. The need to reach new potential consumers in the face of increased production capacity induces qualitative changes in artifact functionality, agent interaction patterns, and the relations between production and consumption. (2) Exaptation. New patterns of interaction among agents around the use of new kinds of artifacts lead to the emergence of new functionality, which in turn induces new kinds of relationships among production, technology, and consumption. (3) Ontological uncertainty. New artifacts, new patterns of interaction around their production and use, and new attributions of functionality generate perpetual novelty in innovation contexts, which makes prediction impossible: not only because agents are unable to decide which among some set of well-defined consequences will happen as a result of actions they contemplate taking, but also because some of the very subjects, objects, and criteria of value with which these consequences of their possible actions would have to be expressed simply do not exist at the historical moment in which agents must act. The paper argues that a theory of innovation capable of providing deep insight into the way in which innovation processes unfold in historical time must begin by embedding these three concepts in its foundation.