This article is concernedwith the calciumsilicate hydrates, including crystallineminerals and the extremely variable and poorly ordered phase (C-S-H)\ud that is the main binding phase in most concrete. Up-to-date composition and crystal-structure information is tabulated for the most important crystalline\ud calcium(alumino) silicate hydrates and related phases.Anumber ofmodels for the nanostructure of C-S-H are summarized and compared and it is shown\ud that there is much more of a consensus than might seem apparent at first sight. The value of the recently solved structures of 1.4 nm tobermorite and\ud jennite, together with those of jaffeite and metajennite, for visualizing the nanostructural elements present in themodels is demonstrated. The importance\ud of Hal Taylor's contribution to the solution of the structure of jennite is highlighted. The applicability of Richardson and Groves' model is demonstrated\ud using experimental composition-structure observations on the nature of C-S-H in a Portland cement-fly ash blend.