© 2020 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd Pig organ xenotransplantation offers a solution to the shortage of deceased human organs for transplantation. The pathobiological response to a pig xenograft is complex, involving antibody, complement, coagulation, inflammatory, and cellular responses. To overcome these barriers, genetic manipulation of the organ-source pigs has largely been directed to two major aims—(a) deletion of expression of the known carbohydrate xenoantigens against which humans have natural (preformed) antibodies, and (b) transgenic expression of human protective proteins, for example, complement- and coagulation-regulatory proteins. Conventional (FDA-approved) immunosuppressive therapy is unsuccessful in preventing an adaptive immune response to pig cells, but blockade of the CD40:CD154 costimulation pathway is successful. Survival of genetically engineered pig kidneys in immunosuppressed nonhuman primates can now be measured in months. Non-immunological aspects, for example, pig renal function, a hypovolemia syndrome, and rapid growth of the pig kidney after transplantation, are briefly discussed. We suggest that patients on the wait-list for a deceased human kidney graft who are unlikely to receive one due to long waiting times are those for whom kidney xenotransplantation might first be considered. The potential risk of infection, public attitudes to xenotransplantation, and ethical, regulatory, and financial aspects are briefly addressed.