Solute transport, defined here as the movement of chemicals in soils and groundwater aquifers, plays a central role in biogeochemical cycling and many other processes. Solute transport can be dominated by advection, diffusion, or dispersion, or by any combination of these. The interaction of a chemical with soil or aquifer solids can slow transport by retardation. The Advection-Dispersion Equation and its two-region or two-site variants have traditionally been applied to solute transport. More modern approaches generalize the Advection-Dispersion Equation. Despite decades of intensive research, our a priori capability to predict solute transport in complex porous media such as soils remains limited.