This paper reports about current mainstream growth projections for the United States and the European Union over the medium term represent a marked slowdown from growth rates in the decades prior to the global financial crisis. Slower growth in Europe and the United States has mixed implications for growth prospects in developing economies. Most obviously, on the negative side, it means less demand for these countries’ exports, so models of development based on export-led growth may need to be rethought. In contrast, for Western Europe the narrative is about catch-up growth rather than the rate of cutting-edge technological progress. From the middle of the 20th century to the recent global crisis, this experience comprised three distinct phases. European medium-term growth prospects depend both on how fast productivity grows in the United States and whether catch-up growth can resume after a long hiatus. Economic historians see social capability as a key determinant of success or failure in catch-up growth.