This paper surveys the empirical literature on the links between innovation, market structure and firm size. The review shows that there is little evidence in support of the Schumpeterian hypothesis that market power and large firms stimulate innovations: R&D spending seems to rise more or less proportionally with firm size after a certain threshold level has been passed, and there is little evidence of a positive relationship between R&D intensity and concentration in general. However, positive linkages between concentration/size and innovative activity can occur when certain conditions are met, including high sunk costs per individual project, economies of scale and scope in the production of innovation rents. Recent empirical work suggests that R&D intensity and market structure are jointly determined by technology, the characteristics of demand, the institutional framework, strategic interaction and chance ...