A fundamental process in the immune response to infection is the activation of T cells following contact with antigen presenting cells. This activation occurs after T cell receptors on the surface of T cells bind to immunogenic peptides expressed on the surface of antigen presenting cells. The binding of T cell receptors to ligands not only leads to the activation of T cells, it is also key to T cell selection in the thymus and the maintenance of a diverse T cell receptor repertoire. T cell receptor bindings are converted into a signal which activates a T cell but there is no universal theory which governs this process. There is experimental evidence to suggest that receptor-ligand bindings must be sufficiently long to elicit a T cell response. and that counting devices in the T cell work to allow signal accumulation, decoding and translation into biological responses. In view of these results, this thesis uses mathematical models to explore the timescales associated with T cell responses. A stochastic criterion that T cell responses occur after N receptor-ligand complexes have been bound for at least a dwell time, T, each, is used. The first model of receptor-ligand binding, in conjunction with the stochastic criterion, supports the affinity threshold hypothesis for thymic selection and agrees with the experimentally established ligand hierarchy for thymic negative selection. The initial model of ligand-receptor binding is then extended to include feedback responses, bivalent receptor binding and ligand diffusion through the immunological synapse. By including these mechanisms, the models agree with an array of experimental hypotheses which include: T cells exhibit a digital response to ligand. bivalent T cell receptor engagement stabilises receptor-ligand bindings and one ligand is sufficient to elicit a T cell response.