Polyploidy has played a central role in plant genome evolution and in the formation of new species such as tetraploid pasta wheat and hexaploid bread wheat. Until recently, the high sequence conservation between homoeologous genes, together with the large genome size of polyploid wheat, had hindered genomic analyses in this important crop species. In the past 5 yr, however, the advent of next-generation sequencing has radically changed the wheat genomics landscape. Here, we review a series of advances in genomic resources and tools for functional genomics that are shifting the paradigm of what is possible in wheat molecular genetics and breeding. We discuss how understanding the relationship between homoeologues can inform approaches to modulate the response of quantitative traits in polyploid wheat; we also argue that functional redundancy has ‘locked up’ a wide range of phenotypic variation in wheat. We explore how genomics provides key tools to inform targeted manipulation of multiple homoeologues, thereby allowing researchers and plant breeders to unlock the full polyploid potential of wheat.