There is a powerful trend in museums today of asking visitors to participate in the exhibitions, co‐create content, and to be active and engage with one another in the museum space. While welcoming the participatory agenda as an initiative of democratizing art museums, we argue in this paper that the rise of the participatory agenda also redefines the purpose of the art museum in a way that risks overlooking the kinds of experiences people undergo in art museums. Based on qualitative and phenomenologically inspired interviews with museum visitors, we present a sketch of a class of aesthetic experiences that ought to be taken into consideration in curatorial practices. Developing a picture of the phenomenology of aesthetic experience, we argue that such experiences should be taken into account when considering the question of the purpose of the art museum.