The most basic economic theory suggests that rising incomes in developing countries will deter emigration from those countries, an idea that captivates policymakers in international aid and trade diplomacy. A lengthy literature and recent data suggest something quite different: that over the course of a "mobility transition", emigration generally rises with economic development until countries reach upper-middle income, and only thereafter falls. This note quantifies the shape of the mobility transition in every decade since 1960. It then briefly surveys 45 years of research, which has yielded six classes of theory to explain the mobility transition and numerous tests of its existence and characteristics in both macro- and micro-level data. The note concludes by suggesting five questions that require further study.