Fibrils of alpha-synuclein are significant components of cellular inclusions associated with several neuropathological disorders including Parkinson's disease, multiple system atrophy and dementia with Lewy bodies. In recent years, technological advances in the field of transmission electron microscopy and image processing have made it possible to solve the structure of alpha-synuclein fibrils at high resolution. This review discusses the results of structural studies using cryo-electron microscopy, which revealed that in-vitro produced fibrils vary in diameter from 5nm for single-protofilament fibrils, to 10nm for two-protofilament fibrils. In addition, the atomic models hint at contributions of the familial Parkinson's disease mutation sites to inter-protofilament interaction and the locations where post-translational modifications take place. Here, we propose a nomenclature system that allows identifying the existing alpha-synuclein polymorphs and that will allow to incorporate additional high-resolution structures determined in the future.