Data sharing in current P2P systems is very much restricted to file-system-like capabilities. In this paper, we present the strategies that we have adopted in our BestPeer project to support more fine-grained data sharing, especially, relational data sharing, in a P2P context. First, we look at some of the issues in designing a peer-based data management system, and discuss some possible solutions to address these issues. Second, we present the design of our first prototype system, PeerDB, and report our experience with it. Finally, we discuss our current extensions to PeerDB to support keyword-based queries.