The domestication of wheat in the Fertile Crescent 10,000 years ago led to a genetic bottleneck. Modern agriculture has further narrowed the genetic base by introducing extreme levels of uniformity on a vast spatial and temporal scale. This reduction in genetic complexity renders the crop vulnerable to new and emerging pests and pathogens. The wild relatives of wheat represent an important source of genetic variation for disease resistance. For nearly a century farmers, breeders, and cytogeneticists have sought to access this variation for crop improvement. Several barriers restricting interspecies hybridization and introgression have been overcome, providing the opportunity to tap an extensive reservoir of genetic diversity. Resistance has been introgressed into wheat from at least 52 species from 13 genera, demonstrating the remarkable plasticity of the wheat genome and the importance of such natural variation in wheat breeding. Two main problems hinder the effective deployment of introgressed resistance genes for crop improvement: (1) the simultaneous introduction of genetically linked deleterious traits and (2) the rapid breakdown of resistance when deployed individually. In this review, we discuss how recent advances in molecular genomics are providing new opportunities to overcome these problems.