T cells recognize peptides presented by major histocompatibility complex (MHC) proteins on cell surfaces. Computational prediction of MHC-presented peptides is an essential tool for epitope mapping and vaccine design. In this dissertation, I introduce improved predictors of peptide presentation on MHC class I. The predictors are fit to published datasets of MHC-presented peptides identified by mass spectrometry, as well as other sources. Separate models are developed for predicting MHC/peptide binding and the antigen processing steps that occur prior to MHC binding in vivo. I show that a combination model incorporating these two components achieves higher accuracy than existing methods at predicting MHC presentation, as well as neoantigens recognized by CD8+ T cells from cancer patients. The new methods are made available as an open source software package called MHCflurry (https://github.com/openvax/mhcflurry).