Technical Abstract: Increasing wheat yields to help to ensure food security is a major challenge. Meeting this challenge requires a quantum improvement in the yield potential of wheat. Past increases in yield potential have largely resulted from improvements in harvest index not through increased biomass. Further large increases in harvest index are unlikely, but an opportunity exists for increasing productive biomass and harvestable grain. Photosynthetic capacity and efficiency are a bottleneck to raising productivity and there is strong evidence that increasing photosynthesis will increase crop yields provided that other constraints do not become limiting. Even small increases in the rate of net photosynthesis can translate into large increases in biomass and hence yield, since carbon assimilation is integrated over the entire growing season and crop canopy. This review discusses the strategies to increase photosynthesis that are being proposed by the wheat yield consortium in order to increase wheat yield potential.