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Various hospitals in the U.S. and around the world suffer from the well-known problem of Emergency Department (ED) overcrowding, which prevents them from serving their patients in effective and efficient ways. An important contributor to this problem, which became even more dire after the COVID-19 pandemic, is prolonged boarding of patients who are admitted to inpatient units through the ED. Patients admitted through the ED constitute about 50% of all non-obstetrical hospital admissions in the U.S., and may be boarded in the ED for long hours with the hope of finding an available bed in their primary inpatient unit. In this chapter, we shed light on effective ways of reducing ED boarding times by considering the trade-off between keeping patients in the ED and assigning them to a secondary inpatient unit. The former can increase the risk of adverse events and also cause congestion in the ED (which, in turn, prevents from serving new ED patients in a timely manner), whereas the latter may adversely impact the quality of care post ED service. Further complicating this calculus is the fact that a secondary inpatient unit for a currently boarded ED patient can be the primary unit for a future arriving patient; assignments, therefore, should be made in an orchestrated way. Developing a queueing-based Markov decision process, we demonstrate that patience in transferring patients is a virtue, but only up to a point. We also find that, contrary to the prevalent perception, idling inpatient beds in hospitals can be beneficial (under some circumstances). Since the optimal policy for dynamically assigning patients to their primary and secondary inpatient units is complex and hard to implement in hospitals, we develop a simple policy which we term penalty-adjusted Largest Expected Workload Cost (LEWC-p). Using simulation analyses calibrated with hospital data, we find that implementing this policy could significantly help hospitals to improve their patient safety by reducing boarding times while controlling the overflow of patients to secondary units. Using data analyses and various simulation experiments, we also help hospital administrators by generating insights into hospital conditions under which achievable improvements are significant.