Corals are major contributors to a range of key ecosystem functions on tropical reefs, including calcification, photosynthesis, nutrient cycling, and the provision of habitat structure. The abundance of corals is declining at multiple scales, and the species composition of assemblages is responding to escalating human pressures, including anthropogenic global warming. An urgent challenge is to understand the functional consequences of these shifts in abundance and composition in different biogeographical contexts. While global patterns of coral species richness are well known, the biogeography of coral functions in provinces and domains with high and low redundancy is poorly understood. Here, we quantify the functional traits of all currently recognized zooxanthellate coral species (n = 821) in both the Indo-Pacific and Atlantic domains to examine the relationships between species richness and the diversity and redundancy of functional trait space. We find that trait diversity is remarkably conserved (>75% of the global total) along latitudinal and longitudinal gradients in species richness, falling away only in species-poor provinces (n < 200), such as the Persian Gulf (52% of the global total), Hawaii (37%), the Caribbean (26%), and the East-Pacific (20%), where redundancy is also diminished. In the more species-poor provinces, large and ecologically important areas of trait space are empty, or occupied by just a few, highly distinctive species. These striking biogeographical differences in redundancy could affect the resilience of critical reef functions and highlight the vulnerability of relatively depauperate, peripheral locations, which are often a low priority for targeted conservation efforts. Significance The wide variety of functional trait combinations among the world’s coral faunas can be represented by just a few dimensions of variation. The diversity of coral traits among these dimensions is consistently high along Pacific and Indian Ocean diversity gradients, despite a threefold decline in species richness (from approximately 600 to 200 species). Functional redundancy, defined as multiple species sharing similar arrays of traits, is highest in the central Indo-Pacific biodiversity hotspot. While these Indo-Pacific provinces are globally important reserves of coral reef resilience and function, peripheral species-poor regions are potentially more vulnerable to functional collapse, as indicated by a critical lack of redundancy among species and the reduced capacity for similar species to respond differently to chronic or acute stressors.