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This paper presents a new methodology for assessing the ability of gridded hydrological models to reproduce large-scale hydrological high and low flow events (as a proxy for hydrological extremes) as described by catalogues of historical droughts [using the regional deficiency index (RDI)] and high flows [regional flood index (RFI)] previously derived from river flow measurements across Europe. Using the same methods, total runoff simulated by three global hydrological models from the Water Model Intercomparison Project (WaterMIP) [Joint U.K. Land Environment Simulator (JULES), Water Global Assessment and Prognosis (WaterGAP), and Max Planck Institute Hydrological Model (MPI-HM)] run with the same meteorological input (watch forcing data) at the same spatial 0.5° grid was used to calculate simulated RDI and RFI for the period 1963–2001 in the same European regions, directly comparable with the observed catalogues. Observed and simulated RDI and RFI time series were compared using three performance measures: the relative mean error, the ratio between the standard deviation of simulated over observed series, and the Spearman correlation coefficient. Results show that all models can broadly reproduce the spatiotemporal evolution of hydrological extremes in Europe to varying degrees. JULES tends to produce prolonged, highly spatially coherent events for both high and low flows, with events developing more slowly and reaching and sustaining greater spatial coherence than observed—this could be due to runoff being dominated by slow-responding subsurface flow. In contrast, MPI-HM shows very high variability in the simulated RDI and RFI time series and a more rapid onset of extreme events than observed, in particular for regions with significant water storage capacity—this could be due to possible underrepresentation of infiltration and groundwater storage, with soil saturation reached too quickly. WaterGAP shares some of the issues of variability with MPI-HM—also attributed to insufficient soil storage capacity and surplus effective precipitation being generated as surface runoff—and some strong spatial coherence of simulated events with JULES, but neither of these are dominant. Of the three global models considered here, WaterGAP is arguably best suited to reproduce most regional characteristics of large-scale high and low flow events in Europe. Some systematic weaknesses emerge in all models, in particular for high flows, which could be a product of poor spatial resolution of the input climate data (e.g., where extreme precipitation is driven by local convective storms) or topography. Overall, this study has demonstrated that RDI and RFI are powerful tools that can be used to assess how well large-scale hydrological models reproduce large-scale hydrological extremes—an exercise rarely undertaken in model intercomparisons.