•Sharing economy platforms have a set of essential affordances for mediating exchanges.•Sharing economy platforms can be discussed and compared in terms of centralization.•The literature is preoccupied with centralized, profit-driven platforms like Uber.•Future research must develop a conceptualization of decentralized sharing contexts.•Future research must engage directly with the nature of sharing economy technologies. Over the last few years the sharing economy has been changing the way that people share and conduct transactions in digital spaces. This research phenomenon has drawn scholars from a large number of disparate fields and disciplines into an emerging research area. Given the variety of perspectives represented, there is a great need to collect and connect what has been done, and to identify some common themes, which will serve as a basis for future discussions on the crucial roles played by digital platforms in the sharing economy. Drawing on a collection of 435 publications on the sharing economy and related terms, we identify some trends in the literature and underlying research interests. Specifically, we organize the literature around the concept of platform mediation, and draw a set of essential affordances of sharing economy technologies from the reviewed literature. We present the notion of platform centralization/decentralization as an effective organizing principle for the variety of perspectives on the sharing economy, and also evaluate scholars' treatment of technology itself. Finally, we identify important gaps in the existing literature on the relationship between digital platforms and sharing economy, and provide directions for future investigations.