Wheat (Triticum spp.) is one of the founder crops that likely drove the Neolithic transition to sedentary agrarian societies in the Fertile Crescent more than 10,000 years ago. Identifying genetic modifications underlying wheat's domestication requires knowledge about the genome of its allo-tetraploid progenitor, wild emmer (T. turgidum ssp. dicoccoides). We report a 10.1-gigabase assembly of the 14 chromosomes of wild tetraploid wheat, as well as analyses of gene content, genome architecture, and genetic diversity. With this fully assembled polyploid wheat genome, we identified the causal mutations in Brittle Rachis 1 (TtBtr1) genes controlling shattering, a key domestication trait. A study of genomic diversity among wild and domesticated accessions revealed genomic regions bearing the signature of selection under domestication. This reference assembly will serve as a resource for accelerating the genome-assisted improvement of modern wheat varieties.