Drawing from the economics of two-sided markets, we provide suggestions for the definition of the relevant market in cases involving two-sided platforms, such as media outlets, online intermediaries, payment cards companies, and auction houses. We also discuss when a one-sided approach may be harmless and when instead it can potentially lead to a wrong decision. We then show that the current practice of market definition in two-sided markets is only in part consistent with the above suggestions. Divergence between our suggestions and practice is due to the failure to fully incorporate the lessons from the economic theory of two-sided markets, to the desire to be consistent with previous practice, and to the higher data requirements and the higher complexity of empirical analysis in cases involving two-sided platforms. In particular, competition authorities have failed to recognize the crucial difference between two-sided transaction and non-transaction markets and have been misled by the traditional argument that where there is no price, there is no market.