To understand changes in global mean and extreme streamflow volumes over recent decades, we statistically analyzed runoff and streamflow simulated by the WBM-plus hydrological model using either observational-based meteorological inputs from WATCH Forcing Data (WFD), or bias-corrected inputs from five global climate models (GCMs) provided by the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP). Results show that the bias-corrected GCM inputs yield very good agreement with the observation-based inputs in average magnitude of runoff and streamflow. On global average, the observation-based simulated mean runoff and streamflow both decreased about 1.3% from 1971 to 2001. However, GCM-based simulations yield increasing trends over that period, with an inter-model global average of 1% for mean runoff and 0.9% for mean streamflow. In the GCM-based simulations, relative changes in extreme runoff and extreme streamflow (annual maximum daily values and annual-maximum seven-day streamflow) are slightly greater than those of mean runoff and streamflow, in terms of global and continental averages. Observation-based simulations show increasing trend in mean runoff and streamflow for about one-half of the land areas and decreasing trend for the other half. However, mean and extreme runoff and streamflow based on the GCMs show increasing trend for approximately two-thirds of the global land area and decreasing trend for the other one-third. Further work is needed to understand why GCM simulations appear to indicate trends in streamflow that are more positive than those suggested by climate observations, even where, as in ISI-MIP, bias correction has been applied so that their streamflow climatology is realistic.