Societally relevant weather impacts typically result from compound events, which are rare combinations of weather and climate drivers. Focussing on four event types arising from different combinations of climate variables across space and time, here we illustrate that robust analyses of compound events — such as frequency and uncertainty analysis under present-day and future conditions, event attribution to climate change, and exploration of low-probability-high-impact events — require data with very large sample size. In particular, the required sample is much larger than that needed for analyses of univariate extremes. We demonstrate that Single Model Initial-condition Large Ensemble (SMILE) simulations from multiple climate models, which provide hundreds to thousands of years of weather conditions, are crucial for advancing our assessments of compound events and constructing robust model projections. Combining SMILEs with an improved physical understanding of compound events will ultimately provide practitioners and stakeholders with the best available information on climate risks.