Aggregation cascade for Alzheimer's amyloid-beta peptides, its relevance to neurotoxicity in the course of Alzheimer's disease and experimental methods useful for these studies are discussed. Details of the solid-phase peptide synthesis and sample preparation procedures for Alzheimer's beta-amyloid fibrils are given. Recent progress in obtaining structural constraints on Abeta-fibrils from solid-state NMR and scanning transmission electron microscopy (STEM) data is discussed. Polymorphism of amyloid fibrils and oligomers of the 'Arctic' mutant of Abeta(1-40) was studied by H-1,C-13 solid-state NMR, transmission electron microscopy (TEM) and atomic force microscopy (AFM), and a real-time aggregation of different polymorphs of the peptide was observed with the aid of in situ AFM. Recent results on binding of Cu(II) ions and Al-citrate and Al-ATP complexes to amyloid fibrils, as studied by electron paramagnetic resonance (EPR) and solid-state Al-27 NMR techniques, are also presented. Copyright (C) 2004 John Wiley Sons, Ltd.