The global prevalence of obesity has increased substantially over the past 40 years, from less than 1% in 1975, to 6-8% in 2016, among girls and boys, and from 3% to 11% among men and from 6% to 15% among women over the same time period. Our aim was to consolidate the evidence on the epidemiology of obesity into a conceptual model of the so-called obesity transition. We used illustrative examples from the 30 most populous countries, representing 77·5% of the world's population to propose a four stage model. Stage 1 of the obesity transition is characterised by a higher prevalence of obesity in women than in men, in those with higher socioeconomic status than in those with lower socioeconomic status, and in adults than in children. Many countries in south Asia and sub-Saharan Africa are presently in this stage. In countries in stage 2 of the transition, there has been a large increase in the prevalence among adults, a smaller increase among children, and a narrowing of the gap between sexes and in socioeconomic differences among women. Many Latin American and Middle Eastern countries are presently at this stage. High-income east Asian countries are also at this stage, albeit with a much lower prevalence of obesity. In stage 3 of the transition, the prevalence of obesity among those with lower socioeconomic status surpasses that of those with higher socioeconomic status, and plateaus in prevalence can be observed in women with high socioeconomic status and in children. Most European countries are presently at this stage. There are too few signs of countries entering into the proposed fourth stage of the transition, during which obesity prevalence declines, to establish demographic patterns. This conceptual model is intended to provide guidance to researchers and policy makers in identifying the current stage of the obesity transition in a population, anticipating subpopulations that will develop obesity in the future, and enacting proactive measures to attenuate the transition, taking into consideration local contextual factors.