The development of distributed generation technology is endowing consumers the ability to produce energy and transforming them into "prosumers". This transformation shall improve energy efficiency and pave the way to a low-carbon future. However, it also exerts critical challenges on system operations, such as the wasted backups for volatile renewable generation and the difficulty to predict behavior of prosumers with conflicting interests and privacy concerns. An emerging business model to tackle these challenges is peer-to-peer energy sharing, whose concepts, structures, applications, models, and designs are thoroughly reviewed in this paper, with an outlook of future research to better realize its potentials.