Deadlocks are a rather undesirable situation in a highly automated flexible manufacturing system. Their occurrences often deteriorate the utilization of resources and may lead to catastrophic results in safety-critical systems. This work surveys the open problems in deadlock control for automated manufacturing systems. The focus is deadlock prevention due to its large and continuing stream of efforts. A control strategy is evaluated in terms of computational complexity, behavioral permissiveness, and structural complexity of its deadlock-free supervisor. This study provides readers with a conglomeration of the open problems in this area and facilitates them in finding a suitable topic for their research.