We study a regulation in Chile that mandates warning labels on products whose sugar or calorie concentration exceeds certain thresholds. We document an overall decrease in sugar and calorie intake of 7-9%. To reveal mechanisms, we focus on breakfast cereal. On the demand side, consumers substitute from labeled to unlabeled products, a pattern that is mostly driven by products which consumers mistakenly believed to be healthy. On the supply side, we find substantial reformulation of products and bunching at the thresholds. We develop and estimate an equilibrium model of demand for food and firms' pricing and nutritional choices. We find that food labels increase consumer welfare by 3.8% of total expenditure, and that these effects are enhanced by firms' responses. We then use the model to study alternative policy designs. Under optimal policy thresholds, food labels and sugar taxes generate similar gains in consumer welfare but food labels benefit the poor relatively more.