Improvisation is not limited to the performing arts, but is extended to everyday life situations such as conversations and decision-making. Due to their ubiquitous nature, improvisation skills have received increasing attention from researchers over the last decade. A core challenge is to grasp the complex creative processes involved in improvisation performance. To date, many studies have attempted to provide insight on brain activity and perceptual experiences when perceiving a performance, especially in musical or artistic form. However, watching/listening a performance is quite different than acting in a performance or performing daily-life activities. In this Perspective, we discuss how researchers have often missed key points concerning the study of improvisation skills, especially by ignoring the central role of bodily experiences in their formation. Furthermore, we consider how the study of (neglected) motor component of improvisation performance can provide valuable insights into the underlying nature of creative processes involved in improvisation skills and their acquisition. Finally, we propose a roadmap for studying improvisation from the acquisition of kinematic data in an ecological context to analysis, including the consideration of the coalition of (individual, environmental and task) constraints in the emergence of improvised behaviors.