In this review self-assembling single-walled porphyrin nanotube (SWPNT) models, based on the data of optical spectroscopy, small angle X-ray scattering and cryogenic transmission electron microscopy, are described.l The Short model, suggesting that SWPNT consists of a set of ladder-type “head-to-tail” J-aggregate helices, is demonstrated to be the best to conform to the experimental data. However, this model does not answer fundamental questions on the mechanism and stereometry of tectone binding, on the driving force of J-aggregate twisting into helices and on the nature of bonds between the helices that cannot be solved due to limitations of the used techniques.