The convergence hypothesis has generated a huge empirical literature: this paper critically reviews some of the earlier key findings, clarifies their implications, and relates them to more recent results. Particular attention is devoted to interpreting convergence empirics. The main findings are: (1) The much-heralded uniform 2% rate of convergence could arise for reasons unrelated to the dynamics of eonomic growth. (2) Usual empirical analyses - cross-section (conditional) convergence regressions, time series modelling, panel data analysis - can be misleading for understanding convergence; a model of polarization in economic growth clarifies those difficulties. (3) The data, more revealingly modelled, show persistence and immobility across countries: some evidence supports Baumol's idea of 'convergence clubs'; some evidence shows the poor getting poorer, and the rich richer, with the middle class vanishing. (4) Convergence, unambiguous up to sampling error, is observed across US states.