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Marco Springmann and colleagues warn that we must shift to more plant-based ‘flexitarian’ diets if we are to reduce the food system’s projected greenhouse-gas emissions and meet the targets of the 2015 Paris Agreement (Nature562, 519–525; 2018). We urge countries to work with the United Nations towards a global agreement on food and agriculture that promotes the adoption of such diets, which are more sustainable than meat-based diets and are backed by evidence on healthy eating.