Digital technologies are profoundly reshaping how people relate to unknown others, yet urban studies and geographies of encounter have yet to adequately incorporate these changes into theory and research. Building on a longstanding concern with stranger encounters in social and urban theory, this paper explores how digital technology brings new possibilities and challenges to urban life. With examples ranging from GPS-enabled apps for sex and dating to sharing economy platforms that facilitate the peer-to-peer exchange of services, new practices mediated by digital technology are making many stranger encounters a matter of choice rather than chance, and they are often private as much as they are public. This paper examines these changes to develop a conceptualisation of stranger intimacy as a potentially generative form of encounter involving conditional relations of openness among the unacquainted, through which affective structures of knowing, providing, befriending or even loving are built. We offer an agenda for researching stranger intimacies to better understand their role in generating new kinds of social and economic opportunity, overcoming constraints of space and place, as well as generating dynamics of inclusion and exclusion, privilege and disadvantage. The paper concludes by considering what critical attention to these encounters can offer geographical scholarship and how an emphasis on digital mediation can push research in productive directions.