The main objective of this work was to study the physical processes implied in the moisture transport in hardened cementitious based materials. Understanding such processes is of particular importance for improving the durability of these widely used materials. We focus on white and grey cement pastes CEM I hardened during long periods of time (up to two years) in controlled atmosphere. In order to decouple the physical processes of moisture transport in the intricated multiscales of these cement pastes, we have also considered calibrated porous materials in the range of micro-, meso and macropores. We used a multiscale NMR platform including spectroscopy, high and low field relaxometry and diffusometry. Other complementary techniques like conductivity and X-tomography have been also used. We have insisted on the possibility of controlling in situ the degree of humidity inside the different NMR probes and on the analysis of experimental data to extract representative parameters for the moisture transport. With these techniques and some original theoretical models, we have shown that the geometry and transport are highly related to the local connectivity and control directly the moisture transport on the micro-meso scales by the confinement. We succeed to explain why is so difficult to modify the moisture distribution at the micro-meso pore scales of these cement pastes. This is important for the durability of these widely used materials because more than 80% of the porosity stays in these ranges of pore sizes. We have also answered to the question concerning the impact of the surface properties and local geometries on the moisture dynamics in the micro-mesoscales of these materials. Last, we have shown the easy way of inducing modification of hydration state in the open access of the macroporosity, contrary to the large difficulty of inducing the same changes at the micro and mesoscale.