The term hematopoietic stem cell transplantation (HSCT) has completely replaced the most widespread bone marrow transplantation (BMT). This semantic change is based on the fact that not only hematopoietic stem cells with capacity for regenerating haematopoiesis and the immune system of the recipient are located in the BM. It was later observed that is possible to mobilise these cells into the peripheral blood, with the aid of certain cytokines, and then collect them through the process of aphaeresis. Moreover, hematopoietic stem cells from umbilical cord blood have been used successfully, and their use in on the increase. The main objectives of HSCT are, first, to substitute a defective haematopoietic system for a healthy one and, secondly, to allow the use of chemo and/or radiotherapy treatment at what would otherwise be supralethal doses, re-establishing haematopoiesis through the administration of haematopoietic progenitor cells. The complications of HSCT tend to be the result of the various factors including toxicity, release of certain cytokine, immunological processes associated with allo-HSCT (especially GVHD) and the effect of immunosuppressive drugs, as we discussed below.