Deep knowledge of crop biodiversity is essential to improve global food security. Despite bread wheat serving as a keystone crop worldwide, the population history of bread wheat and its wild relatives (a.k.a. wheats) remains elusive. By analyzing whole-genome sequences of 795 wheats, we found that bread wheat originated southwest of the Caspian Sea ~11,700 years ago and underwent a slow speciation process, lasting ~3,300 years due to persistent gene flow from wild relatives. Soon after, bread wheat spread across Eurasia and reached Europe, South Asia, and East Asia ~7,000 to ~5,000 years ago, shaping a diversified but occasionally convergent adaptive landscape of bread wheat in novel environments. Opposite to cultivated wheat, wild wheat populations have declined by ~82% in the past ~2,000 years due to the food choice shift of humans, and likely continue to drop because of the changing climate. These findings will guide future efforts in protecting and utilizing wheat biodiversity to improve global food security.