Allogeneic haematopoietic stem-cell transplantation (SCT) is a curative therapy for haematological malignancies and inherited disorders of blood cells, such as sickle-cell anaemia. Mature alphabeta T cells that are contained in the allografts reconstitute T-cell immunity and can eradicate malignant cells in the recipient. Unfortunately, these T cells recognize the recipient as 'non-self' and employ a wide range of immune mechanisms to attack recipient tissues in a process known as graft-versus-host disease (GVHD). The full therapeutic potential of allogeneic haematopoietic SCT will not be realized until approaches to minimize GVHD, while maintaining the positive contributions of donor T cells, are developed. This Review focuses on research in mouse models pursued to achieve this goal.