Deep knowledge of crop biodiversity is essential to improving global food security. Despite bread wheat serving as a keystone crop worldwide, the population history of bread wheat and its relatives, both cultivated and wild, remains elusive. By analysing whole-genome sequences of 795 wheat accessions, we found that bread wheat originated from the southwest coast of the Caspian Sea and underwent a slow speciation process, lasting ~3,300 yr owing to persistent gene flow from its relatives. Soon after, bread wheat spread across Eurasia and reached Europe, South Asia and East Asia ~7,000 to ~5,000 yr ago, shaping a diversified but occasionally convergent adaptive landscape in novel environments. By contrast, the cultivated relatives of bread wh...