Analytical solutions of the advection-dispersion equation can provide useful approximate analyses of solute transport in the subsurface, and can be used in inverse analyses to estimate solute transport parameters. The U.S. Salinity Laboratory, in collaboration with several other groups, over the years developed a large number of analytical solutions for solute transport in soils and groundwater, including one- and multidimensional solutions for equilibrium transport, for physical and chemical nonequilibrium transport, for solute transport in structured media, and for the transport of solutes subject to sequential first order decay reactions. Most of the solutions were recently consolidated into the windows-based STANMOD (STudio of ANalytical MODels) computer software package. In this presentation we review some of the analytical solutions, as well as various applications thereof. The solutions often provide excellent approximations for long-term transient field problems. In one hypothetical example we compare the analytical solution for the transport of a four species PCE decay chain (PCE, TCE, DCE, VC) with a more detailed numerical solution for transient flow and transport through a multi-layered soil profile. We show that the analytical solution for the 360-day simulation gives results that are not substantially different from the numerical simulations. This presentation is part of a SSSA symposium honoring the incredible career of Dr. Art Warrick.