The developing immune system in the embryo is programmed to accept all its own tissues as self‐products and not react against them. It has been the aim of transplantation research for the past 40 years to try and manipulate the developed immune system temporarily to a similar status to that in the embryo at the time of an organ graft, so that the organ graft is accepted but immunity generally is not interfered with. Such a state is known as immunological tolerance and can be produced in the laboratory by a number of special techniques, none of which is appropriate for clinical use in organ grafting. In pigs and rats, an allografted liver can sometimes survive permanently without any immunosuppressive treatment in immunologically mature animals.