Data replication is a key technology in distributed data sharing systems, enabling higher availability and performance. This paper surveys optimistic replication algorithms that allow replica contents to diverge in the short term, in order to support concurrent work practices and to tolerate failures in low-quality communication links. The importance of such techniques is increasing as collaboration through wide-area and mobile networks becomes popular. Optimistic replication techniques are different from traditional “pessimistic” ones. Instead of synchronous replica coordination, an optimistic algorithm propagates changes in the background, discovers conflicts after they happen and reaches agreement on the final contents incrementally. We explore the solution space for optimistic replication algorithms. This paper identifies key challenges facing optimistic replication systems – ordering operations, detecting and resolving conflicts, propagating changes efficiently, and bounding replica divergence – and provides a comprehensive survey of techniques developed for addressing these challenges.