Structural genome variation is a major determinant of useful trait diversity. We describe how genome analysis methods are enabling discovery of trait-associated structural variants and their potential impact on breeding. As our understanding of complex crop genomes continues to grow, there is growing evidence that structural genome variation plays a major role in determining traits important for breeding and agriculture. Identifying the extent and impact of structural variants in crop genomes is becoming increasingly feasible with ongoing advances in the sophistication of genome sequencing technologies, particularly as it becomes easier to generate accurate long sequence reads on a genome-wide scale. In this article, we discuss the origins of structural genome variation in crops from ancient and recent genome duplication and polyploidization events and review high-throughput methods to assay such variants in crop populations in order to find associations with phenotypic traits. There is increasing evidence from such studies that gene presence-absence and copy number variation resulting from segmental chromosome exchanges may be at the heart of adaptive variation of crops to counter abiotic and biotic stress factors. We present examples from major crops that demonstrate the potential of pangenomic diversity as a key resource for future plant breeding for resilience and sustainability.