This dissertation focuses on recording, maintaining and exploiting provenance information in Collaborative Data Sharing Systems (CDSS). These are systems that support data sharing across loosely-coupled, heterogeneous collections of relational databases related by declarative schema mappings. A fundamental challenge in a CDSS is to support the capability of update exchange --- which publishes a participant's updates and then translates others' updates to the participant's local schema and imports them --- while tolerating disagreement between them and recording the provenance of exchanged data, i.e., information about the sources and mappings involved in their propagation. This provenance information can be useful during update exchange, e.g., to evaluate provenance-based trust policies. It can also be exploited after update exchange, to answer a variety of user queries, about the quality, uncertainty or authority of the data, for applications such as trust assessment, ranking for keyword search over databases, or query answering in probabilistic databases. To address these challenges, in this dissertation we develop a novel model of provenance graphs that is informative enough to satisfy the needs of CDSS users and captures the semantics of query answering on various forms of annotated relations. We extend techniques from data integration, data exchange, incremental view maintenance and view update to define the formal semantics of unidirectional and bidirectional update exchange. We develop algorithms to perform update exchange incrementally while maintaining provenance information. We present strategies for implementing our techniques over an RDBMS and experimentally demonstrate their viability in the Orchestra prototype system. We define ProQL, a query language for provenance graphs that can be used by CDSS users to combine data querying with provenance testing as well as to compute annotations for their data, based on their provenance, that are useful for a variety of applications. Finally, we develop a prototype implementation ProQL over an RDBMS and indexing techniques to speed up provenance querying, evaluate experimentally the performance of provenance querying and the benefits of our indexing techniques.