The central questions of karst hydrology concern (1) recharge, storage, and flow of groundwater in contemporary aquifers, (2) identification of geologic constraints on groundwater storage and flow paths, and (3) understanding of how aquifers evolve through time and the relation of this evolution to the evolution of interconnected surface-water basins. Karst aquifers generally display matrix, fracture, and conduit permeability with contrasts in effective hydraulic conductivity of many orders of magnitude. Dispersed recharge into the matrix and fracture permeability provides most of the storage and a slow-response flow system, while point recharge into the conduit system provides quick flow and little storage. A current question is how to describe these components of permeability and the interchange of groundwater between them. Groundwater basins can be delineated by tracer studies and geologic boundary conditions. Progress is being made on the quantitative, fluid mechanics description of conduit flow. The evolution of karst aquifers is a mainly chemical process, with some transport of insoluble clastics by high-velocity conduit waters. The equilibrium carbonate chemistry has been well established for a long time, including accurate values for equilibrium constants. Conduits, shafts, and solutionally modified fractures are the result of differential dissolution rates. Geochemically satisfactory descriptions of dissolution kinetics have been established, so that the evolution of karst aquifers through time can be accurately described. Overall, a comprehensive model for karst aquifer behavior seems to be within sight.