Current Progress in Organ TransplantationAbout This Hardback Organ transplantation is a medical procedure in which an organ is transferred from the body of a donor to that of a recipient. It can be used to replace a damaged or missing organ. Organs and tissues can also be transplanted within the same person's body. These are called autografts. Transplants done between two individuals of the same species are called allografts. Organs can be sourced either from a living or a cadaveric source.