In this review four parameters relevant to the grafting of hemopoietic stem cells (HSC) are analyzed: the nature and amounts of grafted HSC, the sources of HSC and the "in vivo" fate of the grafted cells. One may oppose cells with short-term repopulating ability to cells with long-term reconstitutive capacity. The former comprise progenitors, while the latter consist of primitive stem cells, corresponding to murine pre-colony forming units-spleen (pre-CFU-S) (and to some murine CFU-S) or to human pre-colony forming units (pre-CFU). In the mouse, the number of progenitors involved in short-term reconstitution is large, while that of primitive cells operating months after the transplantation is reduced. These results may be extrapolated to humans, suggesting that it is possible to engraft a limited number of genetically modified HSC. However, the administration of large numbers of reconstituting cells appears to be a cautionary procedure, since it should insure polyclonal hemopoiesis, which is the physiological situation in mammals. Besides marrow, peripheral blood from adult patients treated with chemotherapy and growth factors, and cord blood from newborns, are promising sources of HSC. Successful engraftment depends not only on the quality and quantity of HSC, but also on the integrity of the marrow microenvironment. This microenvironment may be impaired by chemo- and radiotherapy, which provides a theoretical basis for the transplantation of stromal cells along with that of HSC.