Transplantation of organs and tissues provides the clinician with treatment options for many types of organ failure. However, nearly all transplant efforts are limited by a relative scarcity of donor material. Donor organ and tissue availability can be increased by developing suitable preservation methods and by improving the awareness of primary health care providers as to the needs and scope of therapeutic transplantation. Donor material capable of immediate function upon implantation will become available as increasingly effective techniques of tissue and organ preservation develop. These techniques are extremely important for lung, heart, and liver transplantation, where no artificial, long-term methods of support exist, making immediate function a necessity. In Part I of this article, the authors discuss the transplantation of cornea, kidney, heart, lung, and heart-lung block: Part II covers transplantation of liver, pancreas, skin, and bone marrow.