Peptide-MHC (pMHC) complexes are central components of the immune system, and understanding the mechanism behind stable pMHC binding will aid the development of immunotherapies. Stable pMHC binding can be assessed through an analysis of structure, which contain information on the atomic interactions present between peptide and MHC. However, a large-scale analysis of pMHCs is difficult to perform, due to the lack of available structures as well as fact that pMHCs are large molecular systems with slow timescales. This thesis presents a set of approaches developed to deliver scalable structural analysis of Class I pMHC systems. First, we present APE-Gen, a fast method for generating ensembles of bound pMHC conformations. Next, we present a structure-based classifier using random forests for predicting stable pMHC binding. Finally, we present a simulation framework for generating a Markov state model of the full binding dynamics for a given pMHC system using a combination of umbrella and adaptive sampling. This work pushes the capability of computational methods for the structural analysis of pMHCs, leading to structural insight that can guide the understanding of pMHC binding.