T cells are essential immune cells responsible for identifying and eliminating pathogens. Through interactions between their T-cell antigen receptors (TCRs) and antigens presented by major histocompatibility complex molecules (MHCs) or MHC-like molecules, T cells discriminate foreign and self peptides. Determining the fundamental principles that govern these interactions has important implications in numerous medical contexts. However, reconstructing a map between T cells and their antagonist antigens remains an open challenge for the field of immunology, and success of in silico reconstructions of this relationship has remained incremental. In this Perspective, we discuss the role that new state-of-the-art deep-learning models for predicting protein structure may play in resolving some of the unanswered questions the field faces linking TCR and peptide–MHC properties to T-cell specificity. We provide a comprehensive overview of structural databases and the evolution of predictive models, and highlight the breakthrough AlphaFold provided the field.