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In recent years, Operations Research/Management (OR/OM) has had a significant impact on improving the performance of hospital Emergency Departments (EDs). This includes improving a wide range of processes involving patient flow from the initial call to the ED through disposition, discharge home, or admission to the hospital. We review approximately 350 related papers to (i) demonstrate the influence of OR/OM in EDs, and (ii) assist both researchers and practitioners with the OR/OM techniques already available to optimize ED patient flow. In addition, we elaborate on some practical challenges yet to be addressed. By shedding light on some less studied aspects that can have significant impacts on ED operations, we also discuss important possibilities for future OR/OM researchers.