A fundamental challenge to our understanding of biodiversity is to explain why some groups of species undergo adaptive radiations, diversifying extensively into many and varied species, whereas others do not. Both extrinsic environmental factors (for example, resource availability, climate) and intrinsic lineage-specific traits (for example, behavioural or morphological traits, genetic architecture) influence diversification, but few studies have addressed how such factors interact. Radiations of cichlid fishes in the African Great Lakes provide some of the most dramatic cases of species diversification. However, most cichlid lineages in African lakes have not undergone adaptive radiations. We have compiled data on cichlid colonization and diversification in 46 African lakes, along with lake environmental features and information about the traits of colonizing cichlid lineages, to investigate why adaptive radiation does and does not occur. We find that extrinsic environmental factors related to ecological opportunity and intrinsic lineage-specific traits related to sexual selection both strongly influence whether cichlids radiate.