Data replication is a key technology in distributed systems that enables higher availability and performance. This article surveys optimistic replication algorithms. They allow replica contents to diverge in the short term to support concurrent work practices and 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 deploys algorithms not seen in traditional “pessimistic” systems. 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 article 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.