T cells develop in the thymus and then are exported to the periphery. As one ages, the lymphoid mass of the thymus decreases, and a concomitant decrease in the ability to produce new T cells results. Human immunodeficiency virus (HIV) infects CD4(+) T cells and, hence, can also affect thymic function. Here we discuss experimental techniques and mathematical models that aim to quantify the rate of thymic export. We focus on a recent technique involving the quantification of T-cell receptor excision circles (TRECs). We discuss how proper interpretation of TREC data necessitates the critical development of appropriate mathematical models. We review the theory for interpretation of TREC data during aging, HIV infection, and anti-retroviral treatment. Also, we show how TRECs can be used to accurately quantify thymic output in the context of thymectomy experiments. We show that mathematical models are not only useful but absolutely necessary for these analyses. As such, they should be taken as just another tool in the immunologist's arsenal.