This paper was prepared for a conference on "Growth, capital and new technologies" organized by the Instituto Valenciano de Investigaciones Económicas. A previous version was published in EIB Papers/BEI Cahiers 5(2), 2000, pp. 25-46.This paper surveys the recent literature on convergence across countries and regions. I discuss the main convergence and divergence mechanisms identified in the literature and develop a simple model that illustrates their implications for income dynamics. I then review the existing empirical evidence and discuss its theoretical implications. Early optimism concerning the ability of a human capital-augmented neoclassical model to explain productivity differences across economies has been questioned on the basis of more recent contributions that make use of panel data techniques and obtain theoretically implausible results. Some recent research in this area tries to reconcile these findings with sensible theoretical models by exploring the role of alternative convergence mechanisms and the possible shortcomings of panel data techniques for convergence analysis.Financial support from the European Fund for Regional Development, Fundación Caixa Galicia and the Spanish Ministry of Science and Technology (under grant SEC2002-01612) is gratefully acknowledged.