In the coming decades, larger genetic gains in yield will be necessary to meet projected demand, and this must be achieved despite the destabilizing impacts of climate change on crop production. The root systems of crops capture the water and nutrients needed to support crop growth, and improved root systems tailored to the challenges of specific agricultural environments could improve climate resiliency. Each component of root initiation, growth and development is controlled genetically and responds to the environment, which translates to a complex quantitative system to navigate for the breeder, but also a world of opportunity given the right tools. In this review, we argue that it is important to know more about the ‘hidden half’ of crop plants and hypothesize that crop improvement could be further enhanced using approaches that directly target selection for root system architecture. To explore these issues, we focus predominantly on bread wheat (Triticum aestivum L.), a staple crop that plays a major role in underpinning global food security. We review the tools available for root phenotyping under controlled and field conditions and the use of these platforms alongside modern genetics and genomics resources to dissect the genetic architecture controlling the wheat root system. To contextualize these advances for applied wheat breeding, we explore questions surrounding which root system architectures should be selected for, which agricultural environments and genetic trait configurations of breeding populations are these best suited to, and how might direct selection for these root ideotypes be implemented in practice.