These days, successful transplants happen everyday, but it was a long time before it was possible to do even the simplest procedures successfully.
Transplants are done mostly for life-saving reasons – kidneys, livers, hearts, lungs. But a lot of the easier transplants are not directly life-saving, but help with quality of life instead.
There are myths of early successes, such as Chinese doctor Pien Chi’ao swapping the hearts of two people in order to “achieve balance”, or Christian saints Damian and Cosmas transplanting a recently dead Ethiopian’s leg to replace a Roman priest’s diseased one in the 4th century. These cannot be treated seriously (especially as the Christian saint was known to have died a hundred years before).
16th century surgeon Gaspara Tagliacozzi successfully performed autografts (transplanting of skin from one place to another on the same body), but was unable to perform transplants between people. He thought this had to do with the mind of the person rejecting the foreign material, writing about this in 1596.
In 1823, doctor Carl Bunger transplanted skin from the patient’s inner thigh to the nose, to repair damage caused by syphilis. There is actually a believable account of an Indian surgeon named Sushrata performing almost this exact procedure in the 2nd century BCE.
The first transplant which was done purely to correct a life-threatening deficiency was a thyroid transplant in 1883. The surgeon, Theodor Kocher, had noticed through decades of removing thyroids (for treatment of goiter) that the complete lack of a thyroid lead to a series of symptoms, and found he was able to correct the symptoms by transplanting thyroid tissue back into these people. When the same symptoms were noticed in other people, he found that transplanting thyroid tissue from healthy people into the sick individuals cured those symptoms. This was the first transplant procedure in a modern sense – where the transplanting is done in order to correct a medical issue. Kocher won a Nobel Prize in 1909 for discovering the function of the thyroid gland. This procedure was not a full thytoid gland transplant; simply a transplant of thyroid tissue.
Larger organs were troublesome, though. Alexis Carrel performed successful transplants of arteries and veins, but his tests of transplants of hearts, kidneys, and spleens in dogs highlighted a new problem.
The problem that had first been noticed in 1596 became a problem in the 20th century when surgeons were learning to transplant larger organs. The recipient body was rejecting the donated organs, causing infection as the body’s immune system attacked the large foreign invader. The problem was understood, but there was no known way to overcome the problems, and large organ transplants were abandoned largely because of this.
In 1951, Peter Medawar suggested the use of the drug Cortisone to suppress the immune system during transplant procedures.
Because living people need most of their organs, it is not always possible to obtain an organ for transplanting. The first successful transplant from a dead body was in 1954, when Joseph Murray and J Hartwell Harrison transplanted a kidney from a recipient’s deceased twin. Because the twins were identical, there was no immunosuppression needed.
The ultimate transplant is one in which absolutely everything is transfered from one person to another. A body transplant is the closest thing there is to that, in which a person's head is decapitated and then re-attached to a donor body. The first attempt at an operation of this kind is being planned by a doctor, Sergio Canavero, who claims to have been able to perform the operation on rats and mice already.