The generation of toxic non-native protein conformers has emerged as a unifying thread among disorders such as Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis. Atomic-level detail regarding dynamical changes that facilitate protein aggregation, as well as the structural features of large-scale ordered aggregates and soluble non-native oligomers, would contribute significantly to current understanding of these complex phenomena and offer potential strategies for inhibiting formation of cytotoxic species. However, experimental limitations often preclude the acquisition of high-resolution structural and mechanistic information for aggregating systems. Computational methods, particularly those combine both all-atom and coarse-grained simulations to cover a wide range of time and length scales, have thus emerged as crucial tools for investigating protein aggregation. Here we review the current state of computational methodology for the study of protein self-assembly, with a focus on the application of these methods toward understanding of protein aggregates in human neurodegenerative disorders.