Nonrenewable groundwater resources are of two kinds.  The first comprises aquifer systems of past pluvial climates that are isolated from the modern hydrological cycle either due to deep burial, or due to negligible recharge consequent to extreme aridity.  Water in these systems is analogous to a nonrenewable mineral resource.  The second includes aquifer systems of young sedimentary basins that participate in modern-day hydrological cycle, whose ability to release water from storage may be irreversibly diminished by the very act of extracting water for human use. This paper concerns the latter.  The role of transient storage of water in fine-grained sediments was identified and exemplified by Terzaghi and Meinzer during the 1920s. Their conceptualizations provide the basis for comprehending the behavior of nonrenewable ground water resources.  Aggressive development of ground water from sedimentary basins throughout the United States since the late nineteenth century has led to much ground water mining, and we now have a body of reliable data indicating how transient subsurface storage space has been irretrievably lost.  This paper begins by examining the evolution of ideas on the mechanics of water-saturated sediments, followed by a review of information available on storage depletion from confining layers of some large sedimentary basins.  Finally, the implications of current knowledge to water resource management are examined. Ultimately, the challenge of nonrenewable ground water is about managing retrievable storage space of aquifer systems, and about hydrogeochemical changes that can potentially occur due to large scale mixing of waters of contrasting chemical attributes across aquifer-aquitard interfaces.