When organs are transplanted from one person to another the main problem is that of the recipient's body not accepting the transplanted organ. This leads to the body's defense mechanism attacking the organ like it would attack any other foreign body and destroying it.
To prevent organ rejection, it is first essential to test the compatibility of the donor and the recipient. Only if there is a high level of compatibility between the two is the transplantation carried out. If the donor and the recipient are related and have common genes the chances of rejection are reduced to a large extent. An example of this would be identical twins that have the same genetic profile.
In real life, the donor and recipient usually do not have the same genetic profile. To reduce rejection and extend the life of the transplanted organ the recipient is given immunosuppressant drugs. This weakens the immune system and saves the transplanted organ; but it simultaneously makes the recipient more susceptible to other illnesses. The use of immunosupressants can be reduced and the organ saved at the same time by avoiding the use of steroids and calcineurin inhibitors, and other treatments specific to each patient.