A summary of some solid state NMR (CP/MAS 13C-NMR) techniques useful for studying isolated cellulose will be discussed and, structural models used for interpreting results will be illustrated by examples. The strong connection between NMR spectra and the supramolecular structure of cellulose will be exemplified and compared with results obtained from similar samples by x-ray scattering techniques (WAXS). NMR and x-ray data recorded on cellulose I isolated from plants can successfully be interpreted by an ‘aggregated square cross-section fibril model’. This interpretation model is consistent with vast amounts of experimental data, both NMR and x-ray, possess an impressive explaining power and remains to be falsified. These properties of the aggregated square cross-section fibril model are surprisingly often overlooked by many researchers working with isolated cellulose I, in favour of poorer ‘home-brewed’ structural models with significantly less experimental support.