In recent decades, empirical study of experience has been installed as a relevant and necessary element in researching cognitive phenomena. However, its incorporation into cognitive science has been largely done by following an objectivist frame of reference, without reconsidering the practices and standards involved in the process of research and the interpretation and validation of the results. This has given rise to a number of issues that reveal inconsistencies in the understanding and treatment of some crucial aspects of first-person research. In this article, we will outline a research direction aiming at contributing to the establishment of a framework for the study of experience that addresses these inconsistencies. Specifically, we will identify some challenges facing the study of experience-in particular those linked to the understanding of memory, expression and description, and intersubjectivity in exploring experience-and propose to reframe them under the epistemological framework of the enactive approach. Moreover, we will explore the prospect of gaining insight into theoretical and methodological strategies for dealing with these issues by extending our vision beyond the field of cognitive science to its neighboring fields, focusing in particular on the field of somatic practices.