Transcription factors are the major agents that read the regulatory sequence information in the genome to initiate changes in expression of specific genes, both in development and in physiological activation responses. Their actions depend on site-specific DNA binding and are largely guided by their individual DNA target sequence specificities. However, their action is far more conditional in a real developmental context than would be expected for simple reading of local genomic DNA sequence, which is common to all cells in the organism. They are constrained by slow-changing chromatin states and by interactions with other transcription factors, which affect their occupancy patterns of potential sites across the genome. These mechanisms lead to emergent discontinuities in function even for transcription factors with minimally changing expression. This is well revealed by diverse lineages of blood cells developing throughout life from hematopoietic stem cells, which use overlapping combinations of transcription factors to drive strongly divergent gene regulation programs. Here, using development of T lymphocytes from hematopoietic multipotent progenitor cells as a focus, recent evidence is reviewed on how binding specificity and dynamics, transcription factor cooperativity, and chromatin state changes impact the effective regulatory functions of key transcription factors including PU.1, Runx1, Notch-RBPJ, and Bcl11b.