The rise in obesity and other food-related chronic diseases has prompted public-health officials of local communities, national governments, and international institutions to pay attention to the regulation of food supply and consumer behavior. A wide range of policy interventions has been proposed and tested since the early 21st century in various countries. The most prominent are food taxation, health education, nutritional labeling, behavioral interventions at point-of-decision, advertising, and regulations of food quality and trade. While the standard neoclassical approach to consumer rationality provides limited arguments in favor of public regulations, the recent development of behavioral economics research extends the scope of regulation to many marketing practices of the food industry. In addition, behavioral economics provides arguments in favor of taxation, easy-to-use front-of-pack labels, and the use of nudges for altering consumer choices. A selective but careful review of the empirical literature on taxation, labeling, and nudges suggests that a policy mixing these tools may produce some health benefits. More specifically, soft-drink taxation, front-of-pack labeling policies, regulations of marketing practices, and eating nudges based on affect or behavior manipulations are often effective methods for reducing unhealthy eating. The economic research faces important challenges. First, the lack of a proper control group and exogenous sources of variations in policy variables make evaluation very difficult. Identification is challenging as well, with data covering short time periods over which markets are observed around slowly moving equilibria. In addition, truly exogenous supply or demand shocks are rare events. Second, structural models of consumer choices cannot provide accurate assessment of the welfare benefits of public policies because they consider perfectly rational agents and often ignore the dynamic aspects of food decisions, especially consumer concerns over health. Being able to obtain better welfare evaluation of policies is a priority. Third, there is a lack of research on the food industry response to public policies. Some studies implement empirical industrial organization models to infer the industry strategic reactions from market data. A fruitful avenue is to extend this approach to analyze other key dimensions of industrial strategies, especially decisions regarding the nutritional quality of food. Finally, the implementation of nutritional policies yields systemic consequences that may be underestimated. They give rise to conflicts between public health and trade objectives and alter the business models of the food sector. This may greatly limit the external validity of ex-ante empirical approaches. Future works may benefit from household-, firm-, and product-level data collected in rapidly developing economies where food markets are characterized by rapid transitions, the supply is often more volatile, and exogenous shocks occur more frequently.