This essay presents an overview of the prevailing theoretical literature on innovation, probes the adequacy of existing theory to guide policy regarding innovation, and sketches some directions for more fruitful theorizing. The focus is on the vast interindustry differences in rates of productivity growth, and other manifestations of differential rates of technological progress across industries. It is argued that the most important policy issues involve finding ways to make the currently lagging sectors more progressive, if in fact that can be done. Theory, to be useful, therefore must organize knowledge and guide research regarding what lies behind the uneven performance of the different economic sectors. In fact prevailing theory cannot do this, for two basic reasons. One is that theory is fragmented, and knowledge and research fall into a number of disjoint intellectual traditions. The second is that the strongest of the research traditions that bear on the differential innovation puzzle, research by economists organized around trying to ‘fit’ production functions and explain how production functions ‘shift’, neglects two central aspects of the problem; that innovation involves uncertainty in an essential way, and that the institutional structure supporting innovation varies greatly from sector to sector. The bulk of the paper is concerned with sketching a theoretical structure that appears to bridge a number of presently separate subfields of study of innovation, and which treats uncertainty and institutional diversity centrally.