The nature of Calcium-Silicate-Hydrate (C-S-H), the binding phase of cement, remains a controversial question. In particular, contrary to the former crystalline model, it was recently proposed that its nanoscale structure was actually amorphous. To elucidate this issue, we analyzed the structure of a realistic simulation of C-S-H, and compared the latter to crystalline tobermorite, a natural analogue to cement, and to an artificial ideal glass. Results clearly support that C-S-H is amorphous. However, its structure shows an intermediate degree of order, retaining some characteristics of the crystal while acquiring an overall glass-like disorder. Thanks to a detailed quantification of order and disorder, we show that its amorphous state mainly arises from its hydration.