© 2020 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd. Xenotransplantation research has made considerable progress in recent years, largely through the increasing availability of pigs with multiple genetic modifications, effective immunosuppressive therapy, and anti-inflammatory therapy to protect pig tissues from the primate immune and inflammatory responses and correct molecular incompatibilities. Further study is required regarding identification and investigation of physiological incompatibilities. Although the exact cause remains uncertain, we and others have observed relatively rapid growth of kidney xenografts after transplantation into nonhuman primates (NHPs). There has also been some evidence of growth, or at least ventricular hypertrophy, of the pig heart after orthotopic transplantation into NHPs. Rapid growth could be problematic, particularly with regard to the heart within the relatively restricted confines of the chest. It has been suggested that the problem of rapid growth of the pig organ after transplantation could be resolved by growth hormone receptor (GHR) gene knockout in the pig. The GHR, although most well-known for regulating growth, has many other biological functions, including regulating metabolism and controlling physiological processes. Genetically modified GHRKO pigs have recently become available. We provide data on their growth compared to comparable pigs that do not include GHRKO, and we have reviewed the literature regarding the effect of GHRKO, and its relevance to xenotransplantation.