CD34 and leukemia: This approach abates TCR αβ T-cell-mediated GvHD, prevents Epstein–Barr virus-driven B cell lymphoproliferative disorders occurring in immunocompromised patients, and allows to transfer to the recipient high numbers of haploidentical CD34+ cells and of mature NK cells and TCR γδ T-cells, which can readily exert protective functions against leukemia cell re-growth and life-threatening infections (63–66).