An intensification of the global water cycle is expected to accompany the anticipated "global warming" of Earth during the coming decades. Models suggest that decreased net surface cooling by longwave radiation will drive increased evaporation and that higher atmospheric temperatures will increase the capacity of the atmosphere for long-distance transport of water vapor. Requirement of mass balance implies that changes in convergence of water-vapor fluxes over the continents must be accompanied by changes in streamflow. Therefore, an increase in global streamflow seems highly likely. The increase can be expected to have a rich structure with respect to region, season, flow regime (e.g., flood, baseflow), and probability. Detection of streamflow change will be confounded by the large amplitude of natural, unforced variability in the water cycle, by direct human modification of continental water fluxes and landscape, by the incompleteness of observational records, and by biospheric feedbacks. Recognition of the multi-dimensional nature of streamflow response to climate change may help us to make sense of the observational record.