Significance Solute transport in porous materials is pertinent to many engineering and industrial applications. This research provides direct characterization of spatiotemporal behavior of solute transport in saturated and unsaturated porous media using high-resolution four-dimensional synchrotron X-ray imaging. This research has two key impacts: 1) we demonstrate a workflow for direct characterization of solute transport in any porous material, which allows better design of fabricated porous materials and detailed characterization of natural porous materials, and 2) we evaluate the underlying assumptions used in the existing theories and identify the major gaps in theories that need to be addressed for better predictive modeling.