In order to examine productivity waves and convergence processes, we study productivity trends, trend breaks, and levels for 13 advanced countries between 1890 and 2012. We highlight two productivity waves, a big one following the second industrial revolution and a smaller one following the ICT revolution. The convergence process has been erratic, halted by inappropriate institutions, technology shocks, financial crises, and above all wars, which led to major productivity level leaps, downwards for countries experiencing war on their soil, and upwards for other countries. Productivity trend breaks have been identified following wars, global financial crises, global supply shocks, and major policy changes. The upward trend break for the U.S. in the mid‐1990s has been confirmed, as has the downward trend break for the euro area in the same period.