Amyloid beta (Aβ of Alzheimer's disease) and α-synuclein (α-Syn of Parkinson's disease) form large fibrils. Evidence is increasing however that much smaller oligomers are more toxic and that these oligomers can form transmembrane ion channels. We have proposed previously that Aβ42 oligomers, annular protofibrils, and ion channels adopt concentric β-barrel molecular structures. Here we extend that hypothesis to the superfamily of α, β, and γ-synucleins. Our models of numerous synuclein oligomers, annular protofibrils, tubular protofibrils, lipoproteins, and ion channels were developed to be consistent with sizes, shapes, molecular weights, and secondary structures of assemblies as determined by electron microscopy and other studies. The models have the following features: (1) all subunits have identical structures and interactions; (2) they are consistent with conventional β-barrel theory; (3) the distance between walls of adjacent β-barrels is between 0.6 and 1.2 nm; (4) hydrogen bonds, salt bridges, interactions among aromatic side-chains, burial and tight packing of hydrophobic side-chains, and aqueous solvent exposure of hydrophilic side-chains are relatively optimal; and (5) residues that are identical among distantly related homologous proteins cluster in the interior of most oligomers whereas residues that are hypervariable are exposed on protein surfaces. Atomic scale models of some assemblies were developed.