The significance of plant and animal domestication cannot be underestimated as it provides the foundation for human civilization as well as Darwin’s evolution theory. Wheat cultivars usually consist of: 1. tetraploid durum wheat, Triticum durum Desf. (BBAA) and 2. hexaploid bread wheat, T. aestivum L. (BBAADD), while wild tetraploid emmer wheat (T. dicoccoides) is considered the progenitor of domesticated emmer (BBAA) and durum. The transition from wild emmer to durum via domesticated emmer is the key model to study wheat domestication. We emplyed genomic data combined with agronomic and morphological trait analysis from wild emmer, domesticated emmer, durum and bread wheat to shed light on the most crucial questions such as what, when, where and why associated with wheat domestication. A likely scenario, based on current study and all other available data, is proposed for wheat domestication: Natufians could have started cultivation of wheat sometime during the period between the Bølling-Allerød and the Younger Dryas, planting with large and heavy-seeded types. The actual domestication process for wheat is probably a rapid one, with the wheat farmers and/or the domesticated seeds likely sweeping the whole Levant in a quick mode.