The purpose of this article is to discuss the applicability of the tobermorite–jennite (T/J) and tobermorite–‘solid-solution’ calcium hydroxide (T/CH) viewpoints for the nanostructure of C-S-H present in real cement pastes. The discussion is facilitated by a consideration of the author's 1992 model, which includes formulations for both structural viewpoints; its relationship to other recent models is outlined. The structural details of the model are clearly illustrated with a number of schematic diagrams. Experimental observations on the nature of C-S-H present in a diverse range of cementitious systems are considered. In some systems, the data can only be accounted for on the T/CH structural viewpoint, whilst in others, both the T/CH and T/J viewpoints could apply. New data from transmission electron microscopy (TEM) are presented. The ‘inner product’ (Ip) C-S-H in relatively large grains of C 3S or alite appears to consist of small globular particles, which are ≈4–8 nm in size in pastes hydrated at 20 °C but smaller at elevated temperatures, ≈3–4 nm. Fibrils of ‘outer product’ (Op) C-S-H in C 3S or β-C 2S pastes appear to consist of aggregations of long thin particles that are about 3 nm in their smallest dimension and of variable length, ranging from a few nanometers to many tens of nanometers. The small size of these particles of C-S-H is likely to result in significant edge effects, which would seem to offer a reasonable explanation for the persistence of Q 0(H) species. This would also explain why there is more Q 0(H) at elevated temperatures, where the particles seem to be smaller, and apparently less in KOH-activated pastes, where the C-S-H has foil-like morphology. In blended cements, a reduction in the mean Ca/Si ratio of the C-S-H results in a change from fibrillar to a crumpled-foil morphology, which suggests strongly that as the Ca/Si ratio is reduced, a transition occurs from essentially one-dimensional growth of the C-S-H particles to two-dimensional; i.e., long thin particles to foils. Foil-like morphology is associated with T-based structure. The C-S-H present in small fully hydrated alite grains, which has high Ca/Si ratio, contains a less dense product with substantial porosity; its morphology is quite similar to the fine foil-like Op C-S-H that forms in water-activated neat slag pastes, which has a low Ca/Si ratio. It is thus plausible that the C-S-H in small alite grains is essentially T-based (and largely dimeric). Since entirely T-based C-S-H is likely to have different properties to C-S-H consisting largely of J-based structure, it is possible that the C-S-H in small fully reacted grains will have different properties to the C-S-H formed elsewhere in a paste; this could have important implications.