Drought is a spatio-temporal phenomenon; however, due to limitations of traditional statistical techniques it is often analyzed solely temporally—for instance, by taking the hydroclimate average over a spatial area to produce a timeseries. Herein, we use machine learning based Markov Random Field methods that identify drought in three-dimensional space-time. Critically, the joint space-time character of this technique allows both the temporal and spatial characteristics of drought to be analyzed. We apply these methods to climate model output from the Coupled Model Intercomparison Project phase 5 and tree-ring based reconstructions of hydroclimate over the full Northern Hemisphere for the past 1000 years. Analyzing reconstructed and simulated drought in this context provides a paleoclimate constraint on the spatio-temporal character of past and future droughts, with some surprising and important insights into future drought projections. Climate models, for instance, suggest large increases in the severity and length of future droughts but little change in their width (latitudinal and longitudinal extent). These models, however, exhibit biases in the mean width of drought over large parts of the Northern Hemisphere, which may undermine their usefulness for future projections. Despite these limitations, and in contrast to previous high-profile claims, there are no fundamental differences in the spatio-temporal character of simulated and reconstructed drought during the historical interval (1850-present), with critical implications for our confidence in future projections derived from climate models.