Ordered protein aggregation in the brain is a hallmark of Alzheimer's disease and scrapie. The disease-specific amyloid fibrils comprise primarily a single protein, amyloid β, in Alzheimer's disease, and the prion protein in scrapie. These proteins can be induced to form aggregates in vitro that are indistinguishable from brain-derived fibrils. Consequently, much effort has been invested in the development of in vitro model systems to study the details of the aggregation processes and the effects of endogenous molecules that have been implicated in disease. Selected studies of this type are reviewed herein. A simple mechanistic model has emerged for both processes that involves a nucleation-dependent polymerization. This mechanism dictates that aggregation is dependent on protein concentration and time. Furthermore, amyloid formation can be seeded by a preformed fibril. The physiological consequences of this mechanism are discussed.