Platform-mediated networks encompass several distinct types of participants, including end users, complementors, platform providers who facilitate users' access to complements, and sponsors who develop platform technologies. Each of these roles can be opened—that is, structured to encourage participation—or closed. This paper reviews factors that motivate decisions to open or close mature platforms. At the platform provider and sponsor levels, these decisions entail: 1) interoperating with established rival platforms; 2) licensing additional platform providers; or 3) broadening sponsorship. With respect to end users and complementors, decisions to open or close a mature platform involve: 1) backward compatibility with prior platform generations; 2) securing exclusive rights to certain complements; or 3) absorbing complements into the core platform. Over time, forces tend to push both proprietary and shared platforms toward hybrid governance models characterized by centralized control over platform technology (i.e., closed sponsorship) and shared responsibility for serving users (i.e., an open provider role).