For many products, platforms enable sellers to transact with buyers. We show that the competitive conditions among sellers shape the market structure in platform industries. If product market competition is tough, sellers avoid competitors by joining different platforms. This allows platforms to sustain high fees and explains why, for example, in some online markets, several homogeneous platforms segment the market. Instead, if product market competition is soft, agglomeration on a single platform emerges, and platforms fight for the dominant position. These insights give rise to novel predictions. For instance, market concentration and fees are negatively correlated in platform industries, which inverts the standard logic of competition.