To improve the understanding of trends in extreme flows related to flood events at the global scale, historical and future changes of annual maxima of 7 d streamflow are investigated, using a comprehensive streamflow archive and six global hydrological models. The models' capacity to characterise trends in annual maxima of 7 d streamflow at the continental and global scale is evaluated across 3666 river gauge locations over the period from 1971 to 2005, focusing on four aspects of trends: (i) mean, (ii) standard deviation, (iii) percentage of locations showing significant trends and (iv) spatial pattern. Compared to observed trends, simulated trends driven by observed climate forcing generally have a higher mean, lower spread and a similar percentage of locations showing significant trends. Models show a low to moderate capacity to simulate spatial patterns of historical trends, with approximately only from 12 % to 25 % of the spatial variance of observed trends across all gauge stations accounted for by the simulations. Interestingly, there are statistically significant differences between trends simulated by global hydrological models (GHMs) forced with observational climate and by those forced by bias-corrected climate model output during the historical period, suggesting the important role of the stochastic natural (decadal, inter-annual) climate variability. Significant differences were found in simulated flood trends when averaged only at gauged locations compared to those averaged across all simulated grid cells, highlighting the potential for bias toward well-observed regions in our understanding of changes in floods. Future climate projections (simulated under the RCP2.6 and RCP6.0 greenhouse gas concentration scenarios) suggest a potentially high level of change in individual regions, with up to 35 % of cells showing a statistically significant trend (increase or decrease; at 10 % significance level) and greater changes indicated for the higher concentration pathway. Importantly, the observed streamflow database under-samples the percentage of locations consistently projected with increased flood hazards under the RCP6.0 greenhouse gas concentration scenario by more than an order of magnitude (0.9 % compared to 11.7 %). This finding indicates a highly uncertain future for both flood-prone communities and decision makers in the context of climate change.