T cells developing in the adult thymus ultimately derive from haematopoietic stem cells in the bone marrow. Here, we summarize research into the identity of the haematopoietic progenitors that leave the bone marrow, migrate through the blood and settle in the thymus to generate T cells. Accumulating data indicate that various different bone-marrow progenitors are T-cell-lineage competent and might contribute to intrathymic T-cell development. Such developmental flexibility implies a mechanism of T-cell-lineage commitment that can operate on a range of T-cell-lineage-competent progenitors, and further indicates that only those T-cell-lineage-competent progenitors able to migrate to, and settle in, the thymus should be considered physiological T-cell progenitors.