A substantial increase in grain yield potential is required, along with better use of water and fertilizer, to ensure food security and environmental protection in future decades. For improvements in photosynthetic capacity to result in additional wheat yield, extra assimilates must be partitioned to developing spikes and grains and/or potential grain weight increased to accommodate the extra assimilates. At the same time, improvement in dry matter partitioning to spikes should ensure that it does not increase stem or root lodging. It is therefore crucial that improvements in structural and reproductive aspects of growth accompany increases in photosynthesis to enhance the net agronomic benefits of genetic modifications. In this article, six complementary approaches are proposed, namely: (i) optimizing developmental pattern to maximize spike fertility and grain number, (ii) optimizing spike growth to maximize grain number and dry matter harvest index, (iii) improving spike fertility through desensitizing floret abortion to environmental cues, (iv) improving potential grain size and grain filling, and (v) improving lodging resistance. Since many of the traits tackled in these approaches interact strongly, an integrative modelling approach is also proposed, to (vi) identify any trade-offs between key traits, hence to define target ideotypes in quantitative terms. The potential for genetic dissection of key traits via quantitative trait loci analysis is discussed for the efficient deployment of existing variation in breeding programmes. These proposals should maximize returns in food production from investments in increased crop biomass by increasing spike fertility, grain number per unit area and harvest index whilst optimizing the trade-offs with potential grain weight and lodging resistance.

While an adequate supply of food can be achieved at present for the current global population, sustaining this into the future will be difficult in the face of a steadily increasing population, increased wealth and a diminishing availability of fertile land and water for agriculture. This problem will be compounded by the new uses of agricultural products, for example, as biofuels. Wheat alone provides ≥20% of the calories and the protein for the world's population, and the value and need to increase the production is recognized widely. Currently, the world average wheat yield is around 3 t/ha but there is considerable variation between countries, with region‐specific factors limiting yield, each requiring individual solutions. Delivering increased yields in any situation is a complex challenge that is unlikely to be solved by single approaches and a multidisciplinary integrated approach to crop improvement is required. There are three specific major challenges: increasing yield potential, protecting yield potential, and increasing resource use efficiency to ensure sustainability. Since the green revolution, yields at the farm gate have stagnated in many countries, or are increasing at less than half the rate required to meet the projected demand. In some countries, large gains can still be achieved by improvements in agronomy, but in many others the yield gains will only be achieved by further genetic improvement. In this overview, the problems and potential solutions for increased wheat yields are discussed, in the context of specific geographic regions, with a particular emphasis on China. The importance and the prospects for improvement of individual traits are presented. It is concluded that there are opportunities for yield increase but a major challenge will be avoiding a simultaneous increase in resource requirements.