In recent decades, musicologists have argued for the socio-historical contingency of the notion of “music improvisation,” and have questioned the usefulness of the terms “improvisation” and “composition” in identifying distinct types of musical practices. This chapter charts the authors quest to find a better way to conceptualize music typically described as “improvised,” to understand more fully what it is about such music that leads to use of the term, and to assess whether, after problematizing the concept, there remains anything of value in its application to musical practices. It presents an alternative way of conceptualizing music-making. The chapter closes with a discussion of how this concept of improvisation functions also in everyday (non-musical) improvisations, such as in conversation and other forms of interaction, and thus, in fact, emerges as being a broad and highly applicable conception of improvisation.