Histocompatibilty is the condition in which the body allows the grafting of tissue or the transfusion of blood without rejection. Ultimately, this means that there is anabsence of interference from the body's immune system.
Histocompatibility is governed by Major Histocompatibility Complex (MHC) molecules. Crudely stated, their purpose is to distinguish "self" from "non-self". More specifically, their primary immunological function is to bind and present antigenic peptides on the surfaces of cells for recognition by antigen-specific T cell receptors.
Controlling and inducing histocompatibility is central to ensuring the success of organ transplants. This field is known as transplantation immunology.