There is currently a very active research on the mechanisms that give rise to the cell selection of lymphocyte precursors by the thymus. This selection is basic for the process of formation of the repertoire of T cells with which an organism is potentially capable of developing an immune response to a foreign antigen, and not doing so when encountering its own antigens. This work pretends to detail some recent advances in the knowledge of the process by which cells are positively or negatively selected by the thymus, to give rise to the T cell repertoire of an individual.