parameter estimates are often used in planning or engineering applications to predict flow and design of aquifer extraction or recharge systems. During a typical pumping test in a horizontally extensive aquifer, a well is pumped at constant volumetric flow rate and head observations are made through time at one or more locations. Pumping test data are presented as time-drawdown or distance-drawdown curves, which are fitted to idealized models to estimate aquifer hydraulic properties. For unconfined aquifers properties of interest include hydraulic conductivity, specific storage, specific yield, and possibly unsaturated flow parameters. When estimating aquifer properties using pumping test drawdown data, one can use a variety of analytical solutions involving different conceptualizations and simplifiying assumptions. Analytical solutions are impacted by their simplifiying assumptions, which limit their applicability to characterize certain types of unconfined aquifers. This review presents the historical evolution of the scientific and engineering thoughts concerning groundwater flow towards a pumping well in unconfined aquifers (also referred to variously as gravity, phreatic, or water table aquifers) from the steady-state solutions of Dupuit to the coupled transient saturated-unsaturated solutions. Although it is sometimes necessary to use gridded numerical models in highly irregular or heterogeneous systems, here we limit our consideration to 