Whole-genome duplications are radical evolutionary events that have driven speciation and adaptation in many taxa. Higher-order polyploids have complex histories often including interspecific hybridization and dynamic genomic changes. This chromosomal reshuffling is poorly understood for most polyploid species, despite their evolutionary and agricultural importance, due to the challenge of distinguishing homologous sequences from each other. I will present our results from dense linkage maps generated with targeted sequence capture to improve the diploid strawberry (Fragaria vesca) reference genome and to disentangle the subgenomes of the wild octoploid progenitors of cultivated strawberry, F. virginiana and F. chiloensis. In contrast to a widely accepted model, we find that one of the four subgenomes originates with the diploid cytoplasm donor F. vesca, one with the diploid F. iinumae, and two with an unknown ancestor close to F. iinumae. Extensive unidirectional introgression has converted the F. iinumae-like subgenomes to be more F. vesca-like, but never the reverse, due either to homoploid hybridization in the F. iinumae-like diploid ancestors or else strong selection spreading F. vesca-like sequence among subgenomes via homeologous exchange. In addition, divergence between homeologous chromosomes has been substantially augmented by interchromosomal rearrangements. Our phylogenetic approach reveals novel aspects of the complicated web of genetic exchanges that occur during polyploid evolution and suggests a path forward for unraveling other agriculturally and ecologically important polyploid genomes.