The paper examines the relationship between competition and economic growth, in the theoretical framework described by endogenous growth models, but with a specific interest in the policy implications. In this perspective, the key issue in the debate can be presented as follows: do competition policies always create the best conditions for promoting innovation and growth? Or do they also produce some disincentives for the investment decisions in R&D, such to limit the development of industries with higher innovation? In order to answer these questions, the paper presents a survey of the theoretical literature on competition and growth and it discusses the main models of endogenous growth, both the ones based on horizontal innovation, such as Romer (1990) or Rivera-Batiz and Romer (1991), and the ones based on vertical innovation, like Aghion and Howitt (1992) or Aghion, Dewatripont and Rey (1997). In particular, specific attention is paid to the most recent models of Schumpeterian growth, which show the existence of a non-linear relationship between competition and growth, by considering either the initial degree of competition (Aghion, Blundell, Bloom, Griffith and Howitt, 2005) or the distance from the technological frontier. (Acemoglu, Aghion and Zilibotti, 2006). Finally, the review of the previous models of endogenous growth allows to draw some conclusions about further and possible developments of research on the relation between product market competition and economic growth.