The reduction in coral cover on many contemporary tropical reefs suggests a different set of coral community assemblages will dominate future reefs. To evaluate the capacity of reef corals to persist over various time scales, we examined coral community dynamics in contemporary, fossil, and simulated future coral reef ecosystems. Based on studies between 1987 and 2012 at two locations in the Caribbean, and between 1981 and 2013 at five locations in the Indo-Pacific, we show that many coral genera declined in abundance, some showed no change in abundance, and a few coral genera increased in abundance. Whether the abundance of a genus declined, increased, or was conserved, was independent of coral family. An analysis of fossil-reef communities in the Caribbean revealed changes in numerical dominance and relative abundances of coral genera, and demonstrated that neither dominance nor taxon was associated with persistence. As coral family was a poor predictor of performance on contemporary reefs, a trait-based, dynamic, multi-patch model was developed to explore the phenotypic basis of ecological performance in a warmer future. Sensitivity analyses revealed that upon exposure to thermal stress, thermal tolerance, growth rate, and longevity were the most important predictors of coral persistence. Together, our results underscore the high variation in the rates and direction of change in coral abundances on contemporary and fossil reefs. Given this variation, it remains possible that coral reefs will be populated by a subset of the present coral fauna in a future that is warmer than the recent past.