This paper critically reviews the empirical literature on economic convergence, focusing on the implications of convergence dynamics and their relation to growth theories. The main findings are: 1. The widely cited 2% annual rate of convergence may arise from reasons unrelated to economic growth dynamics. 2. Traditional empirical methods, such as cross-section convergence regressions, time series modeling, and panel data analysis, can be misleading for understanding convergence. A model of polarization in economic growth clarifies these difficulties. 3. Data, when more carefully modeled, show persistence and immobility across countries. Some evidence supports the concept of "convergence clubs," where the rich become richer and the poor poorer, with the middle class vanishing. 4. Convergence, unambiguous up to sampling error, is observed across US states. The paper argues that interpreting convergence empirics in terms of income distribution dynamics broadens the issues they can address, connecting with policy concerns on persistent inequality, regional stagnation, and capital flows between developed and developing countries.This paper critically reviews the empirical literature on economic convergence, focusing on the implications of convergence dynamics and their relation to growth theories. The main findings are: 1. The widely cited 2% annual rate of convergence may arise from reasons unrelated to economic growth dynamics. 2. Traditional empirical methods, such as cross-section convergence regressions, time series modeling, and panel data analysis, can be misleading for understanding convergence. A model of polarization in economic growth clarifies these difficulties. 3. Data, when more carefully modeled, show persistence and immobility across countries. Some evidence supports the concept of "convergence clubs," where the rich become richer and the poor poorer, with the middle class vanishing. 4. Convergence, unambiguous up to sampling error, is observed across US states. The paper argues that interpreting convergence empirics in terms of income distribution dynamics broadens the issues they can address, connecting with policy concerns on persistent inequality, regional stagnation, and capital flows between developed and developing countries.