This paper explores the incentives for, and the effects of, collusion in prices between two-sided platforms. We characterize the most profitable sustainable agreement when platforms collude on both sides of the market and when they collude on a single side of the market. Under two-sided collusion, prices on both sides are higher than the competitive prices, implying that agents on both sides become worse off as compared to the competitive outcome. An increase in cross-group externalities makes two-sided collusion harder to sustain, and reduces the harm from collusion suffered by the agents on a given side as long as the collusive price on that side is lower than the monopoly price. When platforms collude on a single side of the market, the price on the collusive side is lower (higher) than the competitive price if the magnitude of the cross-group externalities exerted on that side is sufficiently large (small). As a result, one-sided collusion may benefit the agents on the collusive side and harm the agents on the competitive side.