Engineering of stem cell grafts by selection of CD34+ cells has been used in autologous and allogeneic hematopoietic stem cell transplantation (HSCT) for more than two decades. Prevention of severe GvHD in allogeneic HSCT is crucial to reduce the risk of transplant-related mortality and morbidity, and to maintain a high level of quality of life. One approach widely used in clinical practice to reduce incidences of GvHD is the ex vivo removal of T lymphocytes from the graft by selection of CD34+ cells. Moreover, immunoselected CD34+ cells are used to boost engraftment with low risk of developing GvHD in patients exhibiting poor graft function. In autologous HSCT, this method of ex vivo graft manipulation may prevent reinfusion of tumor cells and diseasecausing lymphocytes. Thirtyfour compelling case reports are presented in this book, in which this powerful technology was used in multiple stem cell transplantation settings.