Platforms are everywhere. The rise of Uber, Netflix, and Facebook has attracted a lot of attention to this business model. However, despite its relevance and presence in the digital economy, the definition of platforms, their main characteristics, the intuitions about how they set prices, solve coordination issues, or choose their ownership structure seem to be scattered in many papers. This review attempts to organize the last two decades of research on multisided platforms around three essential elements of platforms: price structure, network effects, and control rights. We highlight which definitions are used in the literature, how they are related to the defining characteristics of platforms, and what research has been made on those characteristics. We pay special attention to the research done on pricing, coordination problems, and ownership structure. We conclude by reviewing the theoretical evidence around monopolization and competition policy in multisided markets.