The resistance or conductance of moisture and ions in cement-based materials largely governs the durability of cement-based materials. Unfortunately, the methods currently available for quantifying these physical phenomena in specimens of meaningful size are rather rudimentary and generally offer insufficient information for characterising the underlying physics. Recently, however, tomographic imaging modalities using distributed measurements have proven successful in capturing transport in large cement-based specimens of varying aggregate and matrix constitutions. In this work, we advance the state-of-the-art in the use of tomography for characterising unsaturated/saturated moisture and ion transport in undamaged and damaged cement-based materials. In this effort, we aim to gain significant insights into the fundamental transport mechanisms of cement-based materials including, for example: dual-permeability flow, matrix-fracture moisture transmittance, salt ingress into discrete and distributed fractures, moisture movement in high-temperature environments, corrosion of reinforcement, and much more.