There is a growing discussion about the "Digital Sharing Economy" (DSE). The pervasiveness of digital platforms and the growing interest in a sharing (rather than ownership) style of consumption have allowed for sharing practices to scale up and become a widespread phenomenon. Digital sharing platforms offer a wide variety of services which appear to be more affordable, efficient, and accessible than their conventional counterparts, making them more attractive in the eyes of consumers. The DSE has manifested itself most remarkably in consumer-to-consumer (C2C) and business-to-consumer (B2C) sharing models. New business models have been created to capture and offer the values driving the emerging sharing trend. The innovative, digitally enabled mode of providing access to resources as a service in the DSE has changed consumption patterns both at micro level, as a change in individual lifestyles, and at macro level, manifested in a transformation of socio-economic structures. These ongoing changes may have both positive and negative implications for society from a sustainability perspective. Recognising that the (potential and actual) impacts of sharing platforms on sustainability have not been studied in a systematic way yet, the present paper aims to develop a systematic insight into this interaction by focusing on the business models emerging around sharing platforms as a central starting point. To achieve this, we use a typology of business models that recognizes the affordances and key attributes of sharing in the DSE. The typology covers both C2C and B2C models of sharing. Based on this typology, we discuss the implications of each type of sharing model for sustainability by asking two central questions: How may the given type of sharing affect resource consumption? And what will be the potential impacts on social practices and structures? We hope that the present study can serve as a guideline for assessing the sustainability impacts of sharing platforms -- either already operating in the market or envisaged. By highlighting the aspects most relevant from a sustainability point of view, we expect to contribute to an evolution of the DSE business models towards sustainable development.