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As more and more producers move to use flexible and agile manufacturing as a way to keep them with a competitive edge, the investigations on deadlock resolution in automated manufacturing have received significant attention for a decade. Deadlock and related blocking phenomena often lead to catastrophic results in automated manufacturing systems. Their efficient handling becomes a necessary condition for a system to gain high productivity. This paper intends to present a tutorial survey of state-of-the art modeling and deadlock control methods for discrete manufacturing systems. It presents the updated results in the areas of deadlock prevention, detection and recovery, and avoidance. It focuses on three modeling methods: digraphs, automata, and Petri nets. Moreover, for each approach, the main and relevant contributions are selected enlightening pros and cons. The paper concludes with the future research needs in this important area in order to bridge the gap between the academic research and industrial needs.