Currently, the standard approach used in most centers to prevent graft-versus-host disease after allogeneic transplantation is based on the combination of a calcineurin inhibitor (cyclosporine or tacrolimus) plus a short course of methotrexate. Unfortunately, this strategy is far from ideal, since the risk of acute GVHD is in the range of 30-40% among patients receiving a matched related donor transplantation and even higher among patients receiving transplantation from an unrelated donor while the incidence of chronic GVHD is 60-70% among patients receiving peripheral blood progenitor cells from either a related or unrelated donor.