The two cultivated allopolyploid cottons, Gossypium hirsutum and Gossypium barbadense, represent a remarkable example of parallel independent domestication, both involving dramatic morphological transformations under selection from wild perennial plants to annualized row crops. Deep resequencing of 643 newly sampled accessions spanning the wild‐to‐domesticated continuum of both species, and their allopolyploid relatives, are combined with existing data to resolve species relationships and elucidate multiple aspects of their parallel domestication. It is confirmed that wild G. hirsutum and G. barbadense were initially domesticated in the Yucatan Peninsula and NW South America, respectively, and subsequently spread under domestication over 4000–8000 years to encompass most of the American tropics. A robust phylogenomic analysis of infraspecific relationships in each species is presented, quantify genetic diversity in both, and describe genetic bottlenecks associated with domestication and subsequent diffusion. As these species became sympatric over the last several millennia, pervasive genome‐wide bidirectional introgression occurred, often with striking asymmetries involving the two co‐resident genomes of these allopolyploids. Diversity scans revealed genomic regions and genes unknowingly targeted during domestication and additional subgenomic asymmetries. These analyses provide a comprehensive depiction of the origin, divergence, and adaptation of cotton, and serve as a rich resource for cotton improvement.