Polyploid wheat consists of four species in two lineages, and all are cultivated, of which common wheat (Triticum aestivum) is most important for our daily diet and global food security. Despite almost century-long studies, many questions remain unanswered about their origin and evolution. The cytoplasm of T. turgidum and T. aestivum was derived from the diploid B-genome donor species and the cytoplasm of T. timopheevii and T. zhukovskyi from the diploid G-genome donor species. We sequenced the chloroplast genome of T. timopheevii to compare with T. aestivum and found numerous recurrent rearrangements and a large number of single-nucleotide and length polymorphisms. We estimated a divergence time of over two million years between the B- and G-genome donor species based on synonymous mutations in single-copy genes. Furthermore, the genotyping of over 1,100 accessions of polyploid wheat and Aegilops species by lineage-polymorphic plasmon markers revealed that the A. speltoides is the donor of the G genome but not of the B genome. The latter was derived from an as yet unknown species. Comparative haplotype analysis suggested that T. timopheevii originated in northern Iraq and went through a genetic bottleneck. Discovery of the natural nuclear-cytoplasm hybrids revealed gene flow between T. turgidum and T. timopheevii, particularly in Turkish-Iraqi populations, which complicated the attempts to identify the B-genome donor using nuclear markers. Compared to A. speltoides, T. timopheevii showed accelerated diversification at several plasmon loci, suggesting cytoplasmic response to the nuclear genome polyploidization shock. Our results shed new lights on origin and evolution of polyploid wheat, and highlight the role of nuclear-cytoplasm interactions and inter-lineage introgression on polyploid speciation.