Extreme events such as natural disasters, financial crashes, and overloaded infrastructures or services collapsing cause severe harm and lasting consequences, especially when they strike by surprise. Providing reliable risk forecasts is crucial for early preparedness, to save lives and ecosystems, and prevent economic recessions. However, foreseeing extreme events is statistically challenging, as they are unprecedented or scarce in historical records, and have complex drivers. Existing methods generally either cannot extrapolate or are not designed for accurate forecasting. This thesis develops novel methodologies for accurately forecasting the conditional risk of extreme events and for understanding their drivers, by combining the extrapolation capabilities of extreme value statistics with the predictive versatility of machine learning and with the insightfulness of causal inference. Its contributions include practical methods for predicting extreme quantiles, high-confidence intervals, and other risk metrics, a method for causal discovery in extreme regimes under confounding, and a study of leading AI weather models during extreme events.