Music is an exclusive feature of humankind. It can be considered as a form of universal communication, only partly comparable to the vocalizations of songbirds. Many trends of research in this field try to address music origins, as well as the genetic bases of musicality. On one hand, several hypotheses have been made on the evolution of music and its role, but there is still debate, and comparative studies suggest a gradual evolution of some abilities underlying musicality in primates. On the other hand, genome-wide studies highlight several genes associated with musical aptitude, confirming a genetic basis for different musical skills which humans show. Moreover, some genes associated with musicality are involved also in singing and song learning in songbirds, suggesting a likely evolutionary convergence between humans and songbirds. This comprehensive review aims at presenting the concept of music as a sociocultural manifestation within the current debate about its biocultural origin and evolutionary function, in the context of the most recent discoveries related to the cross-species genetics of musical production and perception.