Rapid adaptive radiation poses two distinct questions apart from speciation and adaptation: What happens after one speciation event and how do some lineages continue speciating through a rapid burst? We review major features of rapid radiations and their mismatch with theoretical models and speciation mechanisms. The paradox is that the hallmark rapid burst pattern of adaptive radiation is contradicted by most speciation models, which predict continuously decelerating diversification and niche subdivision. Furthermore, it is unclear if and how speciation-promoting mechanisms such as magic traits, phenotype matching, and physical linkage of coadapted alleles promote rapid bursts of speciation. We review additional mechanisms beyond ecological opportunity to explain rapid radiations: ( a ) ancient adaptive alleles and the transporter hypothesis, ( b ) sexual signal complexity, ( c ) fitness landscape connectivity, ( d ) diversity begets diversity, and ( e ) plasticity first. We propose new questions and predictions connecting microevolutionary processes to macroevolutionary patterns through the study of rapid radiations.