Pathways to eradicate global hunger while bending the curve of biodiversity loss unanimously suggest changing to less energy-rich diets, closing yield gaps through agroecological principles, adopting modern breeding technologies to foster stress resilience and yields, as well as minimizing harvest losses and food waste. Against the background of a brief history of global agriculture, we review the available evidence on how the global food system might look given a global temperature increase by 3°. We show that a moderate gain in the area suitable for agriculture is confronted with substantial yield losses through strains on crop physiology, multitrophic interactions, and more frequent extreme events. Self-amplifying feedback are unresolved and might lead to further losses. In light of these uncertainties, we see that complexity is underestimated and more systemic research is needed. Efficiency gains in agriculture, albeit indispensable, will not be enough to achieve food security under severe climate change.