This paper constructs a theory of industry growth to study the implications of knowledge diffusion and selection for innovation policy. Firms’ ideas determine their productivity and stochastically evolve over time. Firms innovate to improve their ideas and endogenously exit if unsuccessful. Entrants adopt the ideas of incumbents. In this model, creative destruction operates through selection: when better ideas are innovated or adopted, they selectively replace worse ideas. Innovation externalities vary based on firm productivity: ideas generated by more productive firms create 1) longer-lasting positive externalities due to knowledge diffusion and 2) stronger negative externalities due to dynamic competition effects. Therefore, the net external effect of innovation is heterogeneous across firms. Quantitatively, this heterogeneity is large when the model is calibrated to firm-level data from US manufacturing and retail trade, and implies first-order considerations for the design of innovation policy.