In this article, I apply a structural‐phenomenological conception of experience and self to the anthropological theorizing of spirit possession. In particular, I argue that a phenomenology of the alien, as elaborated by the philosopher Bernhard Waldenfels, allows for a more differentiated understanding of possession phenomena. Following a characterization of alienness—in conceptual distinction from the more common term “otherness”—as a dimension that necessarily eludes experience, I describe spirit possession as a cultural technology to appropriate the experiential alien by transforming it into the symbolic other. I discuss this relation to the alien in thematic areas central to the anthropology of possession: illness and therapy, symbolism and naming, embodiment and self.