Structural changes of chromosomes are a primary mechanism of genome rearrangement over the course of evolution and detailed knowledge of such changes in a given species and its close relatives should increase the efficiency and precision of chromosome engineering in crop improvement. We have identified sequences bordering each of the main translocation and inversion breakpoints on chromosomes 4A, 5A and 7B of the modern bread wheat genome. The locations of these breakpoints allow, for the first time, a detailed description of the evolutionary origins of these chromosomes at the gene level. Results from this study also demonstrate that, although the strategy of exploiting sorted chromosome arms has dramatically simplified the efforts of wheat genome sequencing, simultaneous analysis of sequences from homoeologous and non-homoeologous chromosomes is essential in understanding the origins of DNA sequences in polyploid species.