The last decades have seen a growing interest and demand for community-centered collaborative systems and platforms. These systems and platforms aim to provide an environment in which users can collaboratively create, share and manage resources. While offering attractive opportunities for online collaboration and information sharing, they also open several security and privacy issues. This has attracted several research efforts towards the design and implementation of novel access control solutions that can handle the complexity introduced by collaboration. Despite these efforts, transition to practice has been hindered by the lack of maturity of the proposed solutions. The access control mechanisms typically adopted by commercial collaborative systems like online social network websites and collaborative editing platforms, are still rather rudimentary and do not provide users with a sufficient control over their resources. This survey examines the growing literature on access control for collaborative systems centered on communities, and identifies the main challenges to be addressed in order to facilitate the adoption of collaborative access control solutions in real-life settings. Based on the literature study, we delineate a roadmap for future research in the area of access control for community-centered collaborative systems.