Researchers interested in studying whether convergence dynamics are in place among regions within the same country have adopted both statistical tools and empirical frameworks developed when studying convergence across different economies. We show that this approach is risky, because when an analysis is conducted at the regional level, the absolute and club convergence processes are more likely to co-exist than in the case of world economies. We propose an empirical approach where the two hypotheses are not taken as competing. Our procedure uncovers periods of convergence and periods of divergence for the three samples we studied: Italy observed at both the regional and provincial levels; EU regions; and world economies. We find a process of absolute convergence for Italian regions from 1951 to 1999, and that their convergence process ends in 1971 after a period which we define as clustering convergence. We also find a process of convergence across European regions from 1977 to 1993; that ends in 1985 in favor of a process of clustering and divergence. Finally, our procedure uncovers a process of absolute convergence from 1964 to 1975 and divergence from 1975 to 1999 in the case of world economies.