GDP has usually been used as a proxy for human well-being. Nevertheless, other social aspects should also be considered, such as life expectancy, infant mortality, educational enrollment and crime issues. With this paper we investigate not only economic convergence but also social convergence between regions in a developing country, Colombia, in the period 1975-2005. We consider several techniques in our analysis: sigma convergence, stochastic kernel estimations, and also several empirical models to find out the beta convergence parameter (cross section and panel estimates, with and without spatial dependence). The main results confirm that we can talk about convergence in Colombia in key social variables, although not in the classic economic variable, GDP per capita. We have also found that spatial auto-correlation reinforces convergence processes through deepening market and social factors, while isolation condemns regions to non-convergence.