Large-scale distributed collaborative applications are getting common as a result of rapid progress in distributed technologies (grid, peer-to-peer, and mobile computing). Peer-to-peer (P2P) systems are particularly interesting for collaborative applications as they can scale without the need for powerful servers. In P2P systems, data storage and processing are distributed across autonomous peers, which can join and leave the network at any time. To provide high data availability in spite of such dynamic behavior, P2P systems rely on data replication. Some replication approaches assume static, read-only data (e.g. music files). Other solutions deal with updates, but they simplify replica management by assuming no update conflicts or single-master replication (i.e. only one copy of the replicated data accepts write operations). P2P advanced applications, which must deal with semantically rich data (e.g. XML documents, relational tables, etc.) using a high-level SQL-like query language, are likely to need more sophisticated capabilities such as multi-master replication (i.e. all replicas accept write operations) and update conflict resolution. These issues are addressed by optimistic replication. Optimistic replication allows asynchronous updating of replicas so that applications can progress even though some nodes are disconnected or have failed. As a result, users can collaborate asynchronously. However, concurrent updates may cause replica divergence and conflicts, which should be reconciled. In this survey, we present an overview of data replication, focusing on the optimistic approach that provides good properties for dynamic environments. We also introduce P2P systems and the replication solutions they implement. In particular, we show that current P2P systems do not provide eventual consistency among replicas in the presence of updates, apart from APPA system, a P2P data management system that we are building.