The first cord blood (CB) transplant was performed in 1988 in a patient with Fanconi anemia. The donor was his HLA-identical sister who was known by pre-natal diagnosis to be HLA identical and not affected by the Fanconi mutation. The CB was collected and cryopreserved at birth. The transplant was successful without GvHD and the patient is currently alive and free of disease more than 15 years after transplant, with full hematologic and immunologic donor reconstitution. At the time of the first transplant, little was known about the biologic properties of CB cells and it was thanks to the pioneering work of H. E. Broxmeyer and E. A. Boyse, who studied the progenitor cell content of CB, and of A. D. Auerbach, who realized the pre-natal diagnosis of Fanconi anemia, that this transplant was possible. Since this first transplant, many questions have been answered but others are still open for further research. For example: would a single CB unit contain enough stem cells to permanently engraft children and adults? Would maternal cell contamination in fetal blood engraft and give severe GvHD? What are the immunologic properties of CB cells? How does it interfere with GvHD, GvL and immune reconstitution? Is the immune immaturity of CB lymphocytes able to overcome the HLA barrier and authorize HLA-mismatched transplants? Is it possible to establish CB banks for unrelated and related transplants? What would be the criteria for collection, quality control and cryopreservation?