The use of animals as donors of tissues and organs for xenotransplantations may help in meeting the increasing demand for organs for human transplantations. Clinical studies indicate that the domestic pig best satisfies the criteria of organ suitability for xenotransplantation. However, the considerable phylogenetic distance between humans and the pig causes tremendous immunological problems after transplantation, thus genetic modifications need to be introduced to the porcine genome, with the aim of reducing xenotransplant immunogenicity. Advances in genetic engineering have facilitated the incorporation of human genes regulating the complement into the porcine genome, knockout of the gene encoding the formation of the Gal antigen (α1,3-galactosyltransferase) or modification of surface proteins in donor cells. The next step is two-fold. Firstly, to inhibit processes of cell-mediated xenograft rejection, involving natural killer cells and macrophages. Secondly, to inhibit rejection caused by the incompatibility of proteins participating in the regulation of the coagulation system, which leads to a disruption of the equilibrium in pro- and anti-coagulant activity. Only a simultaneous incorporation of several gene constructs will make it possible to produce multitransgenic animals whose organs, when transplanted to human recipients, would be resistant to hyperacute and delayed xenograft rejection.