Peptides or proteins convert under some conditions from their soluble forms into highly ordered fibrillar aggregates. Such transitions can give rise to pathological conditions ranging from neurodegenerative disorders to systemic amyloidoses. In this review, we identify the diseases known to be associated with formation of fibrillar aggregates and the specific peptides and proteins involved in each case. We describe, in addition, that living organisms can take advantage of the inherent ability of proteins to form such structures to generate novel and diverse biological functions. We review recent advances toward the elucidation of the structures of amyloid fibrils and the mechanisms of their formation at a molecular level. Finally, we discuss the relative importance of the common main-chain and side-chain interactions in determining the propensities of proteins to aggregate and describe some of the evidence that the oligomeric fibril precursors are the primary origins of pathological behavior.