This paper presents an overview of the literature on 'cumulative growth'. It is argued that, independently of the 'new' growth theory, these models have achieved the nature of 'endogenous' growth models. Their main differences, however, lie in the assumptions about the equilibrium prevailing in the economy. Cumulative growth models do not assume a general equilibrium setting and, thus, the main driving force of growth is demand. Although the natural rate of growth is endogenous (through the effect of induced productivity growth), it can be shown that these models are compatible with a wide set of outcomes concerning the catching-up and convergence issue. In order to do this, we present a model of cumulative causation that, overcoming some of the weaknesses of previous models, allows for catching-up from followers to leader to occur. We also show how the induced productivity growth effect may lead to a faster catching-up rate, contrary to the popular result that it necessarily leads to divergence.