Literature on convergence among Latin American countries is still scarce compared to other regions. Moreover, almost none of the research connects convergence to the economic history of Latin America and the usual finding is one speed of convergence. In this paper I analyze 32 countries and 108 years, more observations than any other study. This long span of data allows me to use economic history to explain, analyze, validate, and understand the results of convergence patterns in the region. I find more than one speed of convergence (clubs) related to the known historical background, country characteristics, and external shocks in the region. I study three important phases, following Thorp (1998): from 1900 to 1930, the exporting phase, from 1931 to 1974, the industrialization phase, and from 1975 to 2007, the globalization phase. During the last two phases, I find strong evidence of convergence among those countries that succeeded in industrializing and/or building good institutions. The reason is that technology dissusion and capital accumulation is easier when these 2 phenomena occur.