We propose an analysis of platform competition based on the academic literature with a view towards competition policy. First, we discuss to which extent competition can emerge in digital markets and show which forms it can take. In particular, we underline the role of dynamics, but also of platform differentiation, consumers multi-homing and beliefs to allow competition in platform markets. Second, we analyse competition policy issues and discuss how rules designed for standard markets can perform in two-sided markets. We show that multi-sided externalities create new opportunities for anti-competitive conducts, often related to pricing and contractual imperfections.