Despite economic growth in the post-World War II period, few developing countries have been able to catch up to the income levels in the United States or other advanced economies. Such countries remain trapped at a relative low- or middle-income level. In this article, the authors redefine the concept of income traps as situations in which income levels relative to the United States remain constantly low and with no clear sign of convergence. This approach allows them to study the issue of economic convergence (or lack of it) directly. The authors describe evidence pointing to the existence of both relative low- and middle-income traps and examine cross-country historical transitions between income groups at the global and regional levels. Finally, they point out challenges to the benchmark neoclassical growth theory, which predicts convergence to the developed world over time, and discuss existing theories with the potential to explain income traps.