Atmospheric CO2 concentration [CO2] has increased from 260 to 280 µmol mol-1 (level during crop domestication up to the industrial revolution) to currently 400 and will reach 550 µmol mol-1 by 2050. C3 crops are expected to benefit from elevated [CO2] (e-CO2) thanks to photosynthesis responsiveness to [CO2] but this may require greater sink capacity. We review recent literature on crop e-CO2 responses, related source-sink interactions, how abiotic stresses potentially interact, and prospects to improve e-CO2 response via breeding or genetic engineering. Several lines of evidence suggest that e-CO2 responsiveness is related either to sink intrinsic capacity or adaptive plasticity, for example, involving enhanced branching. Wild relatives and old cultivars mostly showed lower photosynthetic rates, less downward acclimation of photosynthesis to e-CO2 and responded strongly to e-CO2 due to greater phenotypic plasticity. While reverting to such archaic traits would be an inappropriate strategy for breeding, we argue that substantial enhancement of vegetative sink vigor, inflorescence size and/or number and root sinks will be necessary to fully benefit from e-CO2. Potential ideotype features based on enhanced sinks are discussed. The generic 'feast-famine' sugar signaling pathway may be suited to engineer sink strength tissue-specifically and stage-specifically and help validate ideotype concepts. Finally, we argue that models better accounting for acclimation to e-CO2 are needed to predict which trait combinations should be targeted by breeders for a CO2-rich world.