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This article summarizes the literature on two-sided payment card markets. The general conclusion is that interchange fees can help internalize the complementarity between services on both sides of the market but private platforms set too high interchange fees from a social welfare perspective. Private platforms’ price structure is distored in favor of buyers for several reasons: asymmetric choices between buyers and merchants, merchant internalization and/or platform competition. Furthermore, market power of platforms leads to higher total user prices similar to the case of one-sided markets. Platform competition can help to correct for such market power distortions but may exacerbate the price structure distortions. It is shown that full efficiency in the industry cannot be achieved through regulating the interchange fee. This is because the interchange fee affects only the allocation of the total user price between buyers and sellers. The first-best efficiency also requires a lower total price level due to positive externalities between the two sides. A measure to test whether interchange fees are excessive has been proposed but this measure may be imperfect.