Following a review of the literature evidence, an updated model is presented to describe the kind of nanometer-scale structures that occur in non-graphitizing carbons (also known as chars, biocarbons, and biochars) produced from the carbonization of oxygen-containing precursors (especially carbohydrates and lignocellulosic biomass). This is not intended to be a new model, because it is still essentially the same general model and concepts put forward by Franklin in 1951 and updated through integrating additional experimental evidence, ideas, and key features published over the last 64 years. The updated model uses evidence and concepts from recent publications on graphene oxide and reduced graphene oxide to assist in explaining a potential role of heteroatoms (especially oxygen) in the cross-linking, which is considered important in the development of the distinct nanostructure of non-graphitizing carbons. A three-dimensional molecular/atomic model is presented to approximate the nanostructure formed as carbonization temperatures approach 1000 degrees C. The development of this nanostructure over a range of carbonization temperatures is also described.