Evidence shows the importance of food systems for sustainable development: they are at the nexus that links food security, nutrition, and human health, the viability of ecosystems, climate change, and social justice. However, agricultural policies tend to focus on food supply, and sometimes, on mechanisms to address negative externalities. We propose an alternative. Our starting point is that agriculture and food systems' policies should be aligned to the 2030 Agenda for Sustainable Development. This calls for deep changes in comparison with the paradigms that prevailed when steering the agricultural change in the XXth century. We identify the comprehensive food systems transformation that is needed. It has four parts: first, food systems should enable all people to benefit from nutritious and healthy food. Second, they should reflect sustainable agricultural production and food value chains. Third, they should mitigate climate change and build resilience. Fourth, they should encourage a renaissance of rural territories. The implementation of the transformation relies on (i) suitable metrics to aid decision-making, (ii) synergy of policies through convergence of local and global priorities, and (iii) enhancement of development approaches that focus on territories. We build on the work of the Milano Group, an informal group of experts convened by the UN Secretary General in Milan in 2015. Backed by a literature review, what emerges is a strategic narrative linking climate, agriculture and food, and calling for a deep transformation of food systems at scale. This is critical for achieving the Sustainable Development Goals and the Paris Agreement. The narrative highlights the needed consistency between global actions for sustainable development and numerous local-level innovations. It emphasizes the challenge of designing differentiated paths for food systems transformation responding to local and national expectations. Scientific and operational challenges are associated with the alignment and arbitration of local action within the context of global priorities.