This article reviews recent molecular dynamics simulations of the Alzheimer's amyloid-β protein, the primary component of the amyloid plaques found in the brain of Alzheimer's patients. Different simulation techniques, and their application to the study of monomeric, oligomeric, and fibrillar species is discussed. This review highlights how simulations have acted as an invaluable complement to experiment, providing atomistically detailed structural information about monomer, oligomer, and fibrillar structures, as well as mechanistic insights into the aggregation process of amyloid-β protein in the absence and presence of toxicity and aggregation inhibitors.