Clinical bone marrow transplantation started in 1957 at a time when remarkably little was known about hematopoietic stems cells, immune responses to transplants or the identity of transplant antigens. This review will delineate the substantial increase in knowledge about these three areas gained between then and 1992 when the Ceppellini School course on Bone Marrow Transplantation was held, along with the progress made in clinical application, as well as the stumbling blocks that remained to be overcome by further research to advance knowledge. It will outline the significant progress made between 1992 and the present year, 2019, and the remaining problems.