The classic wheat evolutionary history is one of adaptive radiation of the diploid Triticum/Aegilops species (A, S, D), genome convergence and divergence of the tetraploid (Triticum turgidum AABB, and Triticum timopheevii AAGG) and hexaploid (Triticum aestivum, AABBDD) species. We analyzed Acc-1 (plastid acetyl-CoA carboxylase) and Pgk-1 (plastid 3-phosphoglycerate kinase) genes to determine phylogenetic relationships among Triticum and Aegilops species of the wheat lineage and to establish the timeline of wheat evolution based on gene sequence comparisons. Triticum urartu was confirmed as the A genome donor of tetraploid and hexaploid wheat. The A genome of polyploid wheat diverged from T. urartu less than half a million years ago (MYA), indicating a relatively recent origin of polyploid wheat. The D genome sequences of T. aestivum and Aegilops tauschii are identical, confirming that T. aestivum arose from hybridization of T. turgidum and Ae. tauschii only 8,000 years ago. The diploid Triticum and Aegilops progenitors of the A, B, D, G, and S genomes all radiated 2.5-4.5 MYA. Our data suggest that the Acc-1 and Pgk-1 loci have different histories in different lineages, indicating genome mosaicity and significant intraspecific differentiation. Some loci of the S genome of Aegilops speltoides and the G genome of T. timophevii are closely related, suggesting the same origin of some parts of their genomes. None of the Aegilops genomes analyzed is a close relative of the B genome, so the diploid progenitor of the B genome remains unknown.