A platform matches agents from two sides of a market to create a trading opportunity between them. The agents subscribe to the platform by paying subscription fees which are contingent on their reported private types, and then engage in strategic interactions with their matched partner(s). A matching mechanism of the platform specifies the subscription fees as well as the matching rule which determines the probability that each type of agent on one side is matched with each type on the other side. We characterize optimal matching mechanisms which induce truthful reporting from the agents and maximize the subscription revenue. We show that the optimal mechanisms for a one-to-one trading platform match do not necessarily entail assortative matching, and may employ an alternative matching rule that maximizes the extraction of informational rents of the higher type. We then study an auction platform that matches each seller to two agents, and show that the optimal mechanism entails the combination of negative and positive assortative matching.