T lymphocytes are stimulated when they recognize short peptides bound to class I proteins of the major histocompatibility complex (MHC) protein, as peptide–MHC complexes. Due to the diversity in T-cell receptor (TCR) molecules together with both the peptides and MHC proteins they bind to, it has been difficult to design vaccines and treatments based on these interactions. Machine learning has made some progress in trying to predict the immunogenicity of peptide sequences in the context of specific MHC class I alleles but, as such approaches cannot integrate temporal information and lack explanatory power, their scope will always be limited. Here, we advocate a mechanistic description of antigen presentation and TCR activation which is explanatory, predictive, and quantitative, drawing on modeling approaches that collectively span several length and time scales, being capable of furnishing reliable biological descriptions that are difficult for experimentalists to provide. It is a form of multiscale systems biology. We propose the use of chemical rate equations to describe the time evolution of the foreign and host proteins to explain how the original proteins end up being presented on the cell surface as peptide fragments, while we invoke molecular dynamics to describe the key binding processes on the molecular level, including those of peptide–MHC complexes with TCRs which lie at the heart of the immune response. On each level, complementary methods based on machine learning are available, and we discuss the relationship between these divergent approaches. The pursuit of predictive mechanistic modeling approaches requires experimentalists to adapt their work so as to acquire, store, and expose data that can be used to verify and validate such models.