In Europe, wild wheat relatives of the Triticum-Aegilops complex grow in sympatry with cultivated bread wheat (Triticum aestivum L.) and spontaneous hybridization is known to occur. With the development of transgenic wheat, an understanding of the likelihood and occurrence of hybridization and introgression between wheat and its relatives is needed for use in risk assessment. To assess the probability of wheat to wild relative gene introgression, the distribution and biology of wheat wild relatives and their genome affinity and crossability with bread wheat were reviewed. Twelve of the 22 known Aegilops species, as well as one wild Triticum species, T. monococcum L. subsp. aegilopoides (Link) Thell., are known to occur in Europe near or within wheat cultivation. Five tetraploid species, Ae. cylindrica Host., Ae. triuncialis L., Ae. geniculata Roth., Ae. neglecta Req. ex Berthol., and Ae. biuncialis Vis., have wide distribution in most European countries. Bread wheat, wild Aegilops species, and Triticum species are predominantly autogamous (except Ae. speltoides Tausch, typically allogamous), but outcrossing among species is possible depending on species sympatry, concurrent flowering, and sexual compatibility. Spontaneous hybridization with wheat was reported for most of the tetraploid Aegilops species. The probability of gene transfer and gene retention in hybrid progenies is, however, higher when a gene is located on a shared genome, particularly on the D genome shared with Ae. cylindrica and Ae. ventricosa Tausch. Case-by-case and region-by-region assessments are needed to evaluate the risk associated with production and competitiveness of hybrids and their progeny.