 Organ transplantation raises difficult ethical questions about people’s claims to determine what happens to their bodies before and after death. What are these claims? What would it be to respect them? How should they fit with the claims of organ donors’ families or the needs of people whose own organs have failed? And then how should organs be allocated? Who should get priority and why? As with other topics in applied ethics, satisfactory answers require knowing the relevant facts, in this case about organ transplantation.