Calcium-silicate hydrate (C-S-H) is the main binder in cement and concrete. It starts forming from the early stages of cement hydration and it progressively densifies as cement sets. C-S-H nanoscale building blocks form a cohesive gel, whose structure and mechanics are still poorly understood, in spite of its practical importance. Here we review a statistical physics approach recently developed, which allows us to investigate the C-S-H gel formation under the out-of-equilibrium conditions typical of cement hydration. Our approach is based on colloidal particles, precipitating in the pore solution and interacting with effective forces associated to the ionic environment. We present the evolution of the space filling of C-S-H with different particle interactions and compare them with experimental data at different lime concentrations. Moreover, we discuss the structural features of C-S-H in the mesoscale in terms of the scattering intensity. The comparison of our early stage C-S-H structures with small angle neutron scattering (SANS) experiments shows that long range spatial correlations and structural heterogeneties that develop in that early stages of hydration persist also in the hardened paste.