<p indent="0mm">To continue feeding the increasing global population, the amount of wheat produced in the next <sc>50 years</sc> will need to exceed the total amount of wheat produced over the past <sc>10000 years.</sc> This challenge is coupled with a shrinking resource base and the likely onset of climate change. Moreover, a wheat yield plateau seems to have been reached in many regions, leading to concerns that the increasing global demand will not be met without breeding innovations. Heterosis may be exploited to enhance and stabilize wheat yields, but the commercial application of hybrid wheat has been limited by the low level of heterosis. Although the genetic mechanism underlying wheat heterosis is still uncharacterized, strong heterosis is often related to the high genetic diversity of the parents. Introgressive hybridization is a powerful method for expanding the germplasm base by transferring alien genes into wheat populations, with considerable implications for advancing wheat heterosis. In addition to increasing genetic diversity, introgressed alien genes may exhibit distinct spatiotemporal expression patterns or regulatory characteristics in the receptor genetic background, which may affect heterosis. Wheat has rich wild relatives and an allohexaploid genome structure, which is conducive to gene introgression. Generally, there are two ways to introgress alien genes. First, individual chromosomal segments may be introgressed through homoeologous recombination to generate translocations that are mediated by chromosome engineering. The resulting translocations have limited use in classical wheat breeding because the introgression is accompanied by the loss of the corresponding wheat chromosomal region. However, the introgression may be beneficial for the application of heterosis because it and the corresponding wheat chromosome are maintained. Second, homologous-directed recombination enables the simultaneous introgression of multiple chromosomal regions to substantially reshape the wheat genome structure. The triplication of many genes in wheat (i.e., three homeologs) provides a buffering effect, such that the allelic variation of one of the copies may have only a minor phenotypic effect. In contrast, combining a number of novel introgressed segments in a single genotype produces a significant positive effect in classical wheat breeding. The utility of homologous-directed introgression for the commercial application of hybrid wheat remains unclear. However, the genetic needs vary between classical breeding and the application of heterosis. A high rate of alien introgression may be harmful for classical breeding, but may be beneficial for generating strong heterosis. The genetic base of the three wheat subgenomes can be simultaneously restructured by using re-synthetic hexaploid wheat, which is derived from a cross between tetraploid wheat and <italic>Aegilops tauschii</italic>, as the introgression bridge. Alternatively, the three wheat subgenomes can be independently improved by using the three diploid progenitors and the closely related diploids. The resulting hybrid genomes are named A′, B′ and D′, which may serve as foundational materials for promoting the application of wheat heterosis. Increasing the use of the untapped genetic diversity of<italic> A</italic>.<italic> tauschii</italic> should be prioritized to diversify the wheat D-genome, which is the least diverse wheat subgenome.