Protein aggregation into highly structured amyloid fibrils is associated with various diseases including Alzheimer's disease, Parkinson's disease, and type II diabetes. Amyloids can also have normal biological functions and, in the future, could be used as the basis for novel nanoscale materials. However, a full understanding of the physicochemical forces that drive protein aggregation is still lacking. Such understanding is crucial for the development of drugs that can effectively inhibit aberrant amyloid aggregation and for the directed design of functional amyloids. Atomistic simulations can help understand protein aggregation. In particular, atomistic simulations can be used to study the initial formation of toxic oligomers which are hard to characterize experimentally and to understand the difference in aggregation behavior between different amyloidogenic peptides. Here, we review the latest atomistic simulations of protein aggregation, concentrating on amyloidogenic protein fragments, and provide an outlook for the future in this field.