Since liver transplantation was first performed in 1968 by Starzl et al, advances in case selection, liver surgery, anaesthetics, and immunotherapy have significantly increased the indications for and success of this operation. Liver transplantation is now a standard therapy for many end stage liver disorders as well as acute liver failure. However, while demand for cadaveric organ grafts has increased, in recent years the supply of organs has fallen. This review addresses current controversies resulting from this mismatch. In particular, methods for increasing graft availability and difficulties arising from transplantation in the context of alcohol related cirrhosis, primary liver tumours, and hepatitis C are reviewed. Together these three indications accounted for 42% of liver transplants performed for chronic liver disease in the UK in 2000. Ethical frameworks for making decisions on patients' suitability for liver transplantation have been developed in both the USA and the UK and these are also reviewed.