The common wheat (Triticum aestivum L.) is an allohexaploid crop species originating from the distant hybridization between the cultivated tetraploid wheat (T. turgidum) and the wild diploid grass Aegilops tauschii Cosson. Common wheat inherits the high-yielding potential of tetraploid wheat, extends potential to make diverse food products and has broad adaptability to environments afforded by the incorporation of D genome. Different from diploid crops, common wheat hosts three sub-genomes harboring a large number of repetitive genes and shows a strong capacity of genomic buffering and plasticity. Thus, allelic variation at a single locus often results in an insubstantial effect during wheat improvement. The genetic diversity among three sub-genomes of common wheat was not symmetric, and D sub-genome diversity was the lowest. By simulating the origination process of common wheat, synthetic hexaploid wheat can be produced as a bridge to incorporate the genetic variations of Ae. tauschii and tetraploid wheat into common wheat. In contrast to common wheat, synthetic hexaploid wheat harbors abundant favorable variations and owns new expression characteristics at transcriptome level, which provide novel genetic basis for breeding. Although synthetic hexaploid wheat is to be placed with great expectation, the utility remains very limited in wheat breeding. Cytological instability and poor comprehensive agronomic performance are disadvantaging in breeding utilization. Optimization of the crossing and selecting strategies will promote the application of synthetic hexaploid wheat in common wheat breeding.