This article integrates John Dewey’s Art as Experience, Mikel Dufrenne’s Phenomenology of Aesthetic Experience, and phenomenological interviews with museum visitors to answer what it means to be ‘moved by art’. The interviews point to intense affective and existential experiences, in which encounters with art can be genuinely transformative. We focus on Dufrenne’s notion of ‘adherent reflection’ and Dewey’s notions of ‘doing and undergoing’ to understand the intentional structure and dynamics of such experiences, concluding that being moved contains two merged forms of intentionality: one overt aspect of perceptual intentionality directed at the work, and a covert affective intentionality directed back at oneself in one’s situated existence. These are operational simultaneously but can work in loops, one leading to an intensification of the other and vice versa. As such, these analyses emphasize the value of phenomenological interviews and advance the integration of phenomenological and pragmatist thinking in the context of aesthetic experience.