We review the theoretical underpinnings and the empirical findings of the literature that investigates the effects of innovation on firm survival and firm productivity, which constitute the two main channels through which innovation drives growth. We aim to contribute to the ongoing debate along three paths. First, we discuss the extent to which the theoretical perspectives that inform the empirical models allow for heterogeneity in the effects of R&D/innovation on firm survival and productivity. Secondly, we draw attention to recent modeling and estimation effort that reveals novel sources of heterogeneity, non-linearity and volatility in the gains from R&D/innovation, particularly in terms of its effects on firm survival and productivity. Our third contribution is to link our findings with those from prior reviews to demonstrate how the state of the art is evolving and with what implications for future research.