The study of the relationships between innovation and the competitiveness of industries is an important topic for both, academic research and economic policy. The huge economics literature flourished in the last couple of decades on the subject broadly falls into two distinct research traditions, namely the mainstream R&D spillovers approach and the evolutionary economics view. Both traditions agree on the important role played by innovation and the intersectoral diffusion of advanced knowledge for the competitive performance of industrial sectors. Behind this general agreement, however, the two approaches are radically different. This paper shows that, at a deeper level of analysis, the mainstream and evolutionary views do indeed differ with respect to their theoretical foundations, empirical research and policy implications. In a nutshell, while the mainstream R&D spillover approach is inspired by a traditional view of economic policy based on a market-oriented approach, the evolutionary view is on the contrary consistent with the idea that institutional arrangements and policy interventions do indeed play a fundamental role for shaping innovation patterns and their impacts on the competitiveness of industries.