Most assets are traded in multiple interconnected trading venues. This paper develops an equilibrium model of decentralized markets that accommodates general market structures with coexisting exchanges. There are gains to trade in decentralized markets that have no centralized-market counterparts. Markets in which assets are traded in multiple exchanges, whether they are disjoint or intermediated, can give higher welfare than the centralized market with the same traders and assets. Changes in market structure that lower liquidity may increase the utility of every agent. In decentralized markets, demand substitutability is endogenous and heterogeneous across traders.