The ascomycetous yeasts traditionally referred to as the Saccharomyces sensu stricto complex are a group of closely related species that are isolated by a postzygotic barrier. They can easily hybridize; and their allodiploid hybrids propagate by mitotic divisions as efficiently as the parental strains, but can barely divide by meiosis, and thus rarely produce viable spores (sterile interspecies hybrids). The postzygotic isolation is not effective in allotetraploids that are able to carry out meiosis and produce viable spores (fertile interspecies hybrids). By application of molecular identification methods, double (Saccharomyces cerevisiae x Saccharomyces uvarum and S. cerevisiae x Saccharomyces kudriavzevii) and triple (S. cerevisiae x S. uvarum x S. kudriavzevii) hybrids were recently identified in yeast populations of fermenting grape must and cider in geographically distinct regions. The genetic analysis of these isolates and laboratory-bred hybrids revealed great variability of hybrid genome structures and demonstrated that the alloploid genome of the zygote can undergo drastic changes during mitotic and meiotic divisions of the hybrid cells. This genome-stabilization process involves loss of chromosomes and genes and recombination between the partner genomes. This article briefly reviews the results of the analysis of interspecies hybrids, proposes a model for the mechanism of genome stabilization and highlights the potential of interspecies hybridization in winemaking.