Machine-learning-based methods that identify drought in three-dimensional space–time are applied to climate model simulations and tree-ring-based reconstructions of hydroclimate over the Northern Hemisphere extratropics for the past 1000 years, as well as twenty-first-century projections. Analyzing reconstructed and simulated drought in this context provides a paleoclimate constraint on the spatiotemporal characteristics of simulated droughts. Climate models project that there will be large increases in the persistence and severity of droughts over the coming century, but with little change in their spatial extent. Nevertheless, climate models exhibit biases in the spatiotemporal characteristics of persistent and severe droughts over parts of the Northern Hemisphere. We use the paleoclimate record and results from a linear inverse modeling-based framework to conclude that climate models underestimate the range of potential future hydroclimate states. Complicating this picture, however, are divergent changes in the characteristics of persistent and severe droughts when quantified using different hydroclimate metrics. Collectively our results imply that these divergent responses and the aforementioned biases must be better understood if we are to increase confidence in future hydroclimate projections. Importantly, the novel framework presented herein can be applied to other climate features to robustly describe their spatiotemporal characteristics and provide constraints on future changes to those characteristics.