Musical improvisation is often considered in terms of indeterminacy and freedom. It would thus seem to resist the systemization of a scientific approach. However, as cognitive science is expanding the domain of behaviours it seeks to explain, understanding improvisation scientifically is becoming feasible. This talk examines how improvisation can be understood scientifically and the value of a scientific approach by first considering the concept of improvisation in cultural and historical terms, reframing improvisation in a way that can give rise to scientific hypotheses, reviewing past scientific research on improvisation, and exploring new empirical questions and methods from my own research.