The megadiverse plant family Asteraceae forms an iconic component of island floras including many spectacular radiations, but a global picture of its insular diversity is lacking. Here, we uncover the global biogeographical and evolutionary patterns of Asteraceae on islands to reveal the magnitude and potential causes of their evolutionary success. We compile a global checklist of Asteraceae species native and endemic to islands and combine it with macroecological analyses and a phylogenetic review of island radiations. Asteraceae have a global distribution on islands, comprising approximately 6,000 native island species, with 58% endemics. While diversity of the family on islands is lower than expected given its overall diversity, Asteraceae are the most diverse family on oceanic islands, suggesting an exceptional ability to thrive in isolation. In agreement with island biogeography predictions, native Asteraceae diversity increases with area and decreases with isolation, while endemism increases with both. We identify 39 confirmed island radiations and 69 putative radiations, exceeding numbers for other iconic insular groups. Our results reveal Asteraceae offer immense potential for research in ecology and evolution, given their close tracking of island biogeography expectations, large number of both species and radiations, cosmopolitan distribution, and numerous undiscovered radiations. The largest plant family, Asteraceae, forms an iconic component of many island floras. Here, the authors conduct a macroecological review, showing that Asteraceae have a truly global distribution on islands and are the most diverse plant family on oceanic islands.