Two-sided markets arise when two different types of users may realize gains by interacting with one another through one or more platforms or mediators. We initiate a study of the evolution of such markets. We present an empirical analysis of the value accruing to members of each side of the market, based on the presence of the other side. We codify the range of value curves into a general theoretical model, characterize the equilibrium states of two-sided markets in our model, and prove that each platform will converge to one of these equilibria. We give some early experimental results of the stability of two-sided markets, and close with a theoretical treatment of the formation of different kinds of coalitions in such markets.