Narrative work with people displaced by conflict, and the methods we use to elicit and interpret their stories, offers the possibility to examine a common set of assumptions about place, movement and voice. Forced migration narrative inquiry has always focussed upon people’s movement, but storylines have a strong tendency to resolve this movement through the narrator’s return to settled, bordered life. Our ‘moving stories’ proposal builds on a narrative turn that features the mobile experiences of people whose association with settled life has been redefined through forced displacement. We present examples of diaspora storytelling that suggest how we might shift our lens to recognise circumstances where people’s movement is a key feature of the narrative frame, rather than a temporary condition or problem to be solved. By doing so, we allow ourselves to better see the stories that emerge through and because of mobile strategies and connections.