The amyloid β (Aβ) peptides are 39-42 residue-long peptides found in the senile plaques in the brains of Alzheimer's disease (AD) patients. These peptides self-aggregate in aqueous solution, going from soluble and mainly unstructured monomers to insoluble ordered fibrils. The aggregation process(es) are strongly influenced by environmental conditions. Several lines of evidence indicate that the neurotoxic species are the intermediate oligomeric states appearing along the aggregation pathways. This minireview summarizes recent findings, mainly based on solution and solid-state NMR experiments and electron microscopy, which investigate the molecular structures and characteristics of the Aβ peptides at different stages along the aggregation pathways. We conclude that a hairpin-like conformation constitutes a common motif for the Aβ peptides in most of the described structures. There are certain variations in different hairpin conformations, for example regarding H-bonding partners, which could be one reason for the molecular heterogeneity observed in the aggregated systems. Interacting hairpins are the building blocks of the insoluble fibrils, again with variations in how hairpins are organized in the cross-section of the fibril, perpendicular to the fibril axis. The secondary structure propensities can be seen already in peptide monomers in solution. Unfortunately, detailed structural information about the intermediate oligomeric states is presently not available. In the review, special attention is given to metal ion interactions, particularly the binding constants and ligand structures of Aβ complexes with Cu(II) and Zn(II), since these ions affect the aggregation process(es) and are considered to be involved in the molecular mechanisms underlying AD pathology.