Elastic rebound theory forms the basis of the standard earthquake cycle model and predicts large earthquakes to recur regularly through cycles of strain accumulation and release. Yet few individual earthquake records are sufficiently long to test the theory. Here we characterize the distribution of earthquake interevent times from a global compilation of 80 long-term records. We find that large earthquakes recur more regularly than a random Poisson process on individual fault segments. The majority of Earth's well-studied faults shows weakly periodic and uncorrelated large earthquake recurrence, consistent with the expectations of elastic rebound theory. However, many low activity-rate (annual occurrence rates < 2 × 10 −4) faults show random or clustered earthquake recurrence, which cannot be explained by elastic rebound theory. Plain Language Summary To help society prepare for earthquakes, we use the record of previous earthquakes to forecast the chance of future large earthquakes. A key question is whether large earthquakes on a particular fault recur regularly, randomly, or cluster together in time. Here we compile records from 80 different studies of prehistoric earthquakes. We show that large earthquakes on a particular fault recur more regularly than random, except in regions that experience few earthquakes. This means that for regions that experience many earthquakes, we can forecast future large earthquake occurrence with some degree of skill. In contrast, forecasting large earthquake occurrence in places that experience few earthquakes, and where we expect them least, remains exceptionally difficult.