Increased experience and knowledge in the field of heart transplantation has resulted in continued expansion of this clinical activity. The same experience has served to identify many problems and provided some answers which are in many instances incomplete. The outstanding problems in heart transplantation are firstly the availability of donor organs, secondly, the limited storage of excised donor hearts and thirdly the conundrum of transplant vascular disease as it is manifested in the coronary arteries of the donor heart. Despite these problems, heart transplantation remains a very effective form of treatment particularly for young, well-motivated patients in end-stage heart failure. Although there is considerable agreement on many of the issues relating to heart transplantation, there are several areas of controversy. Neonatal heart transplantation is one example, though with accumulated experience, acceptance of the procedure has grown. The purpose of this article is to provide an overview of the present situation and to highlight areas of controversy and ignorance which require investigation.