This paper was prepared for the 2000 European Investment Bank Conference on Economics and Finance: Regional development policy and convergence in the EU.This paper surveys the recent literature on convergence across countries and regions. We discuss the main convergence and divergence mechanisms identified in the literature and develop a simple model that illustrates their implications for income dynamics. We 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.I gratefully acknowledge financial support from the European Fund for Regional Development, the Spanish Ministry of Education through CICYT grant SEC99-1189 and the European TNR "Specialization vs. diversification: the microeconomics of regional development and the propagation of macroeconomic shocks in Europe."