The identification of T-cell epitopes is key for a complete molecular understanding of immune recognition mechanisms in infectious diseases, autoimmunity and cancer. T-cell epitopes further provide targets for personalized vaccines and T-cell therapy, with several therapeutic applications in cancer immunotherapy and elsewhere. T-cell epitopes consist of short peptides displayed on Major Histocompatibility Complex (MHC) molecules. The recent advances in mass spectrometry (MS) based technologies to profile the ensemble of peptides displayed on MHC molecules - the so-called immunopeptidome - had a major impact on our understanding of antigen presentation and MHC ligands. On the one hand, these techniques enabled researchers to directly identify hundreds of thousands of peptides presented on MHC molecules, including some that elicited T-cell recognition. On the other hand, the data collected in these experiments revealed fundamental properties of antigen presentation pathways and significantly improved our ability to predict naturally presented MHC ligands and T-cell epitopes across the wide spectrum of MHC alleles found in human and other organisms. Here we review recent computational developments to analyze experimentally determined immunopeptidomes and harness these data to improve our understanding of antigen presentation and MHC binding specificities, as well as our ability to predict MHC ligands. We further discuss the strengths and limitations of the latest approaches to move beyond predictions of antigen presentation and tackle the challenges of predicting TCR recognition and immunogenicity.