Summary The global obesity epidemic has been escalating for four decades, yet sustained prevention efforts have barely begun. An emerging science that uses quantitative models has provided key insights into the dynamics of this epidemic, and enabled researchers to combine evidence and to calculate the effect of behaviours, interventions, and policies at several levels—from individual to population. Forecasts suggest that high rates of obesity will affect future population health and economics. Energy gap models have quantified the association of changes in energy intake and expenditure with weight change, and have documented the effect of higher intake on obesity prevalence. Empirical evidence that shows interventions are effective is limited but expanding. We identify several cost-effective policies that governments should prioritise for implementation. Systems science provides a framework for organising the complexity of forces driving the obesity epidemic and has important implications for policy makers. Many parties (such as governments, international organisations, the private sector, and civil society) need to contribute complementary actions in a coordinated approach. Priority actions include policies to improve the food and built environments, cross-cutting actions (such as leadership, healthy public policies, and monitoring), and much greater funding for prevention programmes. Increased investment in population obesity monitoring would improve the accuracy of forecasts and evaluations. The integration of actions within existing systems into both health and non-health sectors (trade, agriculture, transport, urban planning, and development) can greatly increase the influence and sustainability of policies. We call for a sustained worldwide effort to monitor, prevent, and control obesity.