T-cell development in mammals is a model for lineage choice and differentiation from multipotent stem cells. Although T-cell fate choice is promoted by signaling in the thymus through one dominant pathway, the Notch pathway, it entails a complex set of gene regulatory network and chromatin state changes even before the cells begin to express their signature feature, the clonal-specific T-cell receptors (TCRs) for antigen. This review distinguishes three developmental modules for T-cell development, which correspond to cell type specification, TCR expression and selection, and the assignment of cells to different effector types. The first is based on transcriptional regulatory network events, the second is dominated by somatic gene rearrangement and mutation and cell selection, and the third corresponds to establishing a poised state of latent regulator priming through an unknown mechanism. Interestingly, in different lineages, the third module can be deployed at variable times relative to the completion of the first two modules. This review focuses on the gene regulatory network and chromatin-based kinetic constraints that determine activities of transcription factors TCF1, GATA3, PU.1, Bcl11b, Runx1, and E proteins in the primary establishment of T-cell identity.