Deposits of amyloid fibrils characterize a diverse group of human diseases that includes Alzheimer's disease, Creutzfeldt-Jakob disease and type II diabetes. Amyloid fibrils formed from different polypeptides contain a common cross-beta spine. Nevertheless, amyloid fibrils formed from the same polypeptide can occur in a range of structurally different morphologies. The heterogeneity of amyloid fibrils reflects different types of polymorphism: (i) variations in the protofilament number, (ii) variations in the protofilament arrangement and (iii) different polypeptide conformations. Amyloid fibril polymorphism implies that fibril formation can lead, for the same polypeptide sequence, to many different patterns of inter- or intra-residue interactions. This property differs significantly from native, monomeric protein folding reactions that produce, for one protein sequence, only one ordered conformation and only one set of inter-residue interactions.