The development of water supplies from wells was placed on a rational basis with Darcy's development of the law governing the movement of fluids through sands and with Dupuit's application of that law to the problem of radial flow toward a pumped well. As field experience increased, confidence in the applicability of quantitative methods was gained and interest in developing solutions for more complex hydrologic problems was stimulated. An important milestone was Theis' development in 1935 of a solution for the nonsteady flow of ground water, which enabled hydrologists for the first time to predict future changes in ground-water levels resulting from pumping or recharging of wells. In the quarter century since, quantitative ground-water hydrology has been enlarging so rapidly as to discourage the preparation of comprehensive textbooks. This report surveys developments in fluid mechanics that apply to groundwater hydrology. It emphasizes concepts and principles, and the delineation of limits of applicability of mathematical models for analysis of flow systems in the field. It stresses the importance of the geologic variable and its role in governing the flow regimen. The report discusses the origin, occurrence, and motion of underground water in relation to the development of terminology and analytic expressions for selected flow systems. It describes the underlying assumptions necessary for mathematical treatment of these flow systems, with particular reference to the way in which the assumptions limit the validity of the treatment.