Musical improvisation is a sophisticated cognitive process that shares many commonalities with language in stimulus features, social behavior, and neural demands . With a renewed interest in quantifying creative processes facilitated by recent advances in neuroimaging technology, musical improvisation has emerged as an ideal paradigm to study creativity. However, many studies isolate the top-down processes related to creativity from those related to production and auditory perception, leaving the question of how creative behaviours integrate sensory information with higher cognitive processes unanswered. The bottom-up neural correlates of music perception have been extensively quantified, often in tandem with language, comprising a common auditory processing network and analogous networks for parsing semantic and syntactic content from music and speech signals. In studies of spontaneously generated music and language, executive control and goal-directed movement networks are added to the perceptual foundation. This review summarizes previous work on music and speech perception and production, and presents a conceptual model of musical improvisation with known neural correlates. We make recommendations on future directions for the study of social interaction with music and language, and discuss the challenges posed by such endeavours.