Empathy is a psychologically significant phenomenon. It plays a key role in the development of the self, sociality, and prosocial behaviour. The term empathy originated in 19th-century aesthetics, where the concept was seen as an explanation for aesthetic experience. Despite renewed interest in the relation between empathy and aesthetic experiences, investigations into how empathy shapes experiences of art are still scarce. Given this situation, we ask the following three questions: What does one experience when experiencing a work of art empathetically? What is given during such moments? How is consciousness structured in aesthetic empathetic experience? To answer these questions, we analysed five different experiences with visual art using a phenomenological psychological methodology. We found that a complexity of psychologically significant meaning arises from the empathic experience of art. The core aspects of this meaning are captured in a structure incorporating experience of a foreign subjective sense, reliving and affective adherence, interiorisation, pleasure in sharing, and affective understanding. Based on this structure, we argue that aesthetic empathy features a sense of otherness to a degree not previously recognised and that aesthetic empathy is an inherently intersubjective experience in which the spectator is invited to participate and share feelings expressed in the work of art in moments of aesthetic presence.