The domestication of wild emmer wheat led to the selection of modern durum wheat, grown mainly for pasta production. We describe the 10.45 gigabase (Gb) assembly of the genome of durum wheat cultivar Svevo. The assembly enabled genome-wide genetic diversity analyses revealing the changes imposed by thousands of years of empirical selection and breeding. Regions exhibiting strong signatures of genetic divergence associated with domestication and breeding were widespread in the genome with several major diversity losses in the pericentromeric regions. A locus on chromosome 5B carries a gene encoding a metal transporter (TdHMA3-B1) with a non-functional variant causing high accumulation of cadmium in grain. The high-cadmium allele, widespread among durum cultivars but undetected in wild emmer accessions, increased in frequency from domesticated emmer to modern durum wheat. The rapid cloning of TdHMA3-B1 rescues a wild beneficial allele and demonstrates the practical use of the Svevo genome for wheat improvement.