One of the reasons that cancer cells can grow, multiply, and spread is that the body does not recognize them as diseased but accepts them as "self." Immune system cells transplanted from a normal donor can often recognize cancer cells -- particularly those of leukemia patients -- as diseased cells and go to work eliminating them. This phenomenon is called the graft-versus-leukemia or graft-versus-tumor effect, and it is one of the reasons that allogeneic transplants can be curative.
This effect appears to be most powerful in diseases that progress slowly, like chronic leukemia, low-grade lymphoma, and in some cases multiple myeloma, but it is less effective in the rapidly growing acute leukemias. In some patients who relapse after transplant, the disease-killing capability of the donor's white blood cells can be harnessed again, by infusing the patient with more of the donor's white blood cells through donor lymphocyte infusion.