Theoretical considerations suggest that wheat yield potential could be increased by up to 50% through the genetic improvement of radiation use efficiency (RUE). However, to achieve agronomic impacts, structural and reproductive aspects of the crop must be improved in parallel. A Wheat Yield Consortium (WYC) has been convened that fosters linkage between ongoing research platforms in order to develop a cohesive portfolio of activities that will maximize the probability of impact in farmers' fields. Attempts to increase RUE will focus on improving the performance and regulation of Rubisco, introduction of C4-like traits such as CO2-concentrating mechanisms, improvement of light interception, and improvement of photosynthesis at the spike and whole canopy levels. For extra photo-assimilates to translate into increased grain yield, reproductive aspects of growth must be tailored to a range of agro-ecosystems to ensure that stable expression of a high harvest index (HI) is achieved. Adequate partitioning among plant organs will be critical to achieve favourable expression of HI, and to ensure that plants with heavier grain have strong enough stems and roots to avoid lodging. Trait-based hybridization strategies will aim to achieve their simultaneous expression in elite agronomic backgrounds, and wide crossing will be employed to augment genetic diversity where needed; for example, to introduce traits for improving RUE from wild species or C4 crops. Genomic selection approaches will be employed, especially for difficult-to-phenotype traits. Genome-wide selection will be evaluated and is likely to complement crossing of complex but complementary traits by identifying favourable allele combinations among progeny. Products will be delivered to national wheat programmes worldwide via well-established international nursery systems and are expected to make a significant contribution to global food security.