Trade agreements are a major determinant of the operation of food systems. Here, we examine how different aspects of trade can constrain or enable governments' ability to implement food system-level actions aimed at enhancing nutrition and mitigating climate change. Concerning technical aspects, we focus on the potential impact of trade agreements on three major strategies for transforming food systems-namely the removal of market barriers for agricultural commodities, the protection of regulatory policy space and the revision of subsidies. Concerning non-technical aspects, we review the evidence on the political economy of trade to show that coherence between trade-policy goals and public-interest goals, such as nutrition and climate change, involves actors' interests, ideas, and formal and informal institutional processes at various levels. With international agreements to liberalize trade and investment being binding, and recommendations to address malnutrition and climate change being non-binding, there is potential for trade to hinder efforts against malnutrition and climate change. Tempering this will require a deeper understanding of the complex trade-food system--nutrition-climate nexus and a new regulatory framework consistent with such complexity, as well as strategic stakeholder engagement. Trade agreements can constrain or enable governments' ability to implement food system-level actions aimed at improving nutrition and mitigating climate change. The technical and political aspects of trade agreements that interact with food systems are reviewed here, and the coherence between trade policy goals and public interest goals, such as nutrition and climate change, is discussed.