Estimation of the hydraulic properties of aquifers, petroleum reservoir rocks, and soil systems is a fundamental task in many branches of Earth sciences and engineering. The transient diffusion equation proposed by Fourier early in the 19th century for heat conduction in solids constitutes the basis for inverting hydraulic test data collected in the field to estimate the two basic parameters of interest, namely, hydraulic conductivity and hydraulic capacitance. Combining developments in fluid mechanics, heat conduction, and potential theory, the civil engineers of the 19th century, such as Darcy, Dupuit, and Forchheimer, solved many useful problems of steady state seepage of water. Interest soon shifted towards the understanding of the transient flow process. The turn of the century saw Buckingham establish the role of capillary potential in governing moisture movement in partially water-saturated soils. The 1920s saw remarkable developments in several branches of the Earth sciences; Terzaghi's analysis of deformation of water-saturated earth materials, the invention of the tensiometer by Willard Gardner, Meinzer's work on the compressibility of elastic aquifers, and the study of the mechanics of oil and gas reservoirs by Muskat and others. In the 1930s these led to a systematic analysis of pressure transients from aquifers and petroleum reservoirs through the work of Theis and Hurst. The response of a subsurface flow system to a hydraulic perturbation is governed by its geometric attributes as well as its material properties. In inverting field data to estimate hydraulic parameters, one makes the fundamental assumption that the flow geometry is known a priori. This approach has generally served us well in matters relating to resource development primarily concerned with forecasting fluid pressure declines. Over the past two decades, Earth scientists have become increasingly concerned with environmental contamination problems. The resolution of these problems requires that hydraulic characterization be carried out at a much finer spatial scale, for which adequate information on geometric detail is not forthcoming. Traditional methods of interpretation of field data have relied heavily on analytic solutions to specific, highly idealized initial-value problems. The availability of efficient numerical models and versatile spreadsheets of personal computers offer promising opportunities to relax many unavoidable assumptions of analytical solutions and interpret field data much more generally and with fewer assumptions. Currently, a lot of interest is being devoted to the characterization of permeability. However, all groundwater systems are transient on appropriate timescales. The dynamics of groundwater systems cannot be understood without paying attention to capacitance. Much valuable insights about the dynamic attributes of groundwater systems could be gained by long-term passive monitoring of responses of groundwater systems to barometric changes, Earth tides, and ocean tides.