The major threat to human societies posed by undernutrition has been recognised for millennia. Despite substantial economic development and scientific innovation, however, progress in addressing this global challenge has been inadequate. Paradoxically, the last half-century also saw the rapid emergence of obesity, first in high-income countries but now also in low- and middle-income countries. Traditionally, these problems were approached separately, but there is increasing recognition that they have common drivers and need integrated responses. The new nutrition reality comprises a global 'double burden' of malnutrition, where the challenges of food insecurity, nutritional deficiencies and undernutrition coexist and interact with obesity, sedentary behaviour, unhealthy diets and environments that foster unhealthy behaviour. Beyond immediate efforts to prevent and treat malnutrition, what must change in order to reduce the future burden? Here, we present a conceptual framework that focuses on the deeper structural drivers of malnutrition embedded in society, and their interaction with biological mechanisms of appetite regulation and physiological homeostasis. Building on a review of malnutrition in past societies, our framework brings to the fore the power dynamics that characterise contemporary human food systems at many levels. We focus on the concept of agency, the ability of individuals or organisations to pursue their goals. In globalized food systems, the agency of individuals is directly confronted by the agency of several other types of actor, including corporations, governments and supranational institutions. The intakes of energy and nutrients by individuals are powerfully shaped by this 'competition of agency', and we therefore argue that the greatest opportunities to reduce malnutrition lie in rebalancing agency across the competing actors. The effect of the COVID-19 pandemic on food systems and individuals illustrates our conceptual framework. Efforts to improve agency must both drive and respond to complementary efforts to promote and maintain equitable societies and planetary health.