T cells in the immune system are activated by binding to foreign peptides (from an external pathogen) or mutant peptide (derived from endogenous proteins) displayed on the surface of a diseased cell. This triggers a series of intracellular signaling pathways, which ultimately dictate the response of the T cell. The insights from computational models have greatly improved our understanding of the mechanisms that control T-cell activation. In this review, we focus on the use of ordinary differential equation-based mechanistic models to study T-cell activation. We highlight several examples that demonstrate the models' utility in answering specific questions related to T-cell activation signaling, from antigen discrimination to the feedback mechanisms that initiate transcription factor activation. In addition, we describe other modeling approaches that can be combined with mechanistic models to bridge time scales and better understand how intracellular signaling events, which occur on the order of seconds to minutes, influence phenotypic responses of T-cell activation, which occur on the order of hours to days. Overall, through concrete examples, we emphasize how computational modeling can be used to enable the rational design and optimization of immunotherapies.