Structural studies of Alzheimer's amyloid fibrils have revealed information about the structure at different levels. The amyloid-beta peptide has been examined in various solvents and conditions and this has led to a model by which a conformational switching occurs from alpha-helix or random coil, to a beta-sheet structure. Amyloid fibril assembly proceeds by a nucleation dependent pathway leading to elongation of the fibrils. Along this pathway small oligomeric intermediates and short fibrillar structures (protofibrils) have been observed. In cross-section the fibril appears to be composed of several subfibrils or protofilaments. Each of these protofilaments is composed of beta-sheet structure in which hydrogen bonding occurs along the length of the fibre and the beta-strands run perpendicular to the fibre axis. This hierarchy of structure is discussed in this review.