Immunocompetent donor T cells in Allogeneic Haematopoietic Stem Cell grafts mediate acute Graft versus Host Disease (GvHD), still a major cause of recipient morbidity and mortality post transplant. Despite the advent of high resolution HLA-typing and matching at HLA loci, acute GvHD remains a significant problem, even in HLA matched siblings, due primarily to minor histocompatability antigen mismatches. Treatment of GvHD remains ineffective and highly immunosuppressive and the challenge to find effective methods of prevention continues. Non selective removal of donor T cells from the graft has been proven to be effective in preventing GvHD but the beneficial effects of donor T cells, namely effective immune reconstitution and anti tumour activity, are lost. This review considers mechanisms by which acute GvHD may be prevented in the context of the current model of GvHD immunopathogenesis, with a special emphasis on the recent techniques of selective removal or destruction of donor allogeneic T cells that have been described.