The chief aim of this survey is to discuss exception handling models which have been developed for concurrent object systems. In conducting this discussion we rely on the following fundamental principles: exception handling should be associated with structuring techniques; concurrent systems require exception handling which is different from that used in sequential systems; concurrent systems are best structured out of (nested) actions; atomicity of actions is crucial for developing complex systems. In this survey we adhere to the well-known classification of concurrent systems, developed in the 70s by C.A.R. Hoare, J.J. Horning and B. Randell, into cooperative, competitive and disjoint ones. Competitive systems are structured using atomic transactions. Atomic actions are used for structuring cooperative systems. Complex systems in which components can compete and cooperate are structured using Coordinated Atomic actions. The focus of the survey is on outlining models and schemes which combine these action-based structuring approaches with exception handling. In conclusion we emphasise that exception handling models should be adequate to the system development paradigm and structuring approaches used.