The sharing economy proposes a new approach to designing and delivering products and services, that aims at avoiding waste, improving efficiency, and favoring bottom-up change. In this research commentary, we survey the current state of things and propose some directions for research. We first describe the industries, products, and services currently representing the sharing paradigm, the technology platforms enabling it, the business models driving it, and the regulatory issues. We envisage that promising areas of research should include: (1) devising more efficient algorithms; (2) considering ecological and prosocial objective functions; (3) dealing with regulatory issues; (4) expanding the span of research to cover more geographical areas and a wider set of services; and (5) supporting services with more reliable reputation and recommendation systems.