We use Schumpeterian growth theory to account for the divergence in per-capita income that has taken place between countries since the mid-19th Century, as well as for the convergence that took place amongst the richest countries during the second half of the 20th Century. The argument is based on the premise that technological change underwent a fundamental transformation in the 19th Century, associated with new scientific ideas and the increasingly scientific content of new technologies. Countries then sorted themselves into three convergence groups (R&D, Implementation, and Stagnation). A country's group membership depends on initial conditions as well as on fundamentals. JEL codes: O10, O11 Keywords: growth, R&D, convergence, productivity.