Several neurodegenerative diseases are associated with the unfolding and subsequent fibrillization of proteins. Although neither the assembly mechanism nor the atomic structures of the amyloid fibrils are known, recent experimental and computational studies suggest that a few general principles that govern protein aggregation may exist. Analysis of the results of several important recent studies has led to a set of tentative ideas concerning the oligomerization of proteins and peptides. General rules have been described that may be useful in predicting regions of known proteins (prions and transthyretin) that are susceptible to fluctuations, which give rise to structures that can aggregate by the nucleation-growth mechanism. Despite large variations in the sequence-dependent polymerization kinetics of several structurally unrelated proteins, there appear to be only a few plausible scenarios for protein and peptide aggregation.