Transplantation is a preferred treatment over dialysis because of its improved outcomes.
The principal problems in kidney transplantation are immunologic, i.e. avoiding rejection of the transplanted kidney by the recipient's immune system.
The first kidney transplant was done in Boston by surgeon Joseph E. Murray in 1954. (This was the first successful human organ transplant.) Murray removed a kidney from Ronald Herrick and transplanted it to his identical twin, Richard Herrick (and thereby skirted the immunologic problems). In 1990, Murray shared the Nobel Prize in Physiology or Medicine with E. Donnall Thomas "for their discoveries concerning organ and cell transplantation in the treatment of human disease."