Burst-suppression electroencephalography (EEG) patterns of electrical activity, characterized by intermittent high-power broad-spectrum oscillations alternating with isoelectricity, have long been observed in the human brain during general anesthesia, hypothermia, coma and early infantile encephalopathy. Recently, commonalities between conditions associated with burst-suppression patterns have led to new insights into the origin of burst-suppression EEG patterns, their effects on the brain, and their use as a therapeutic tool for protection against deleterious neural states. These insights have been further supported by advances in mechanistic modeling of burst suppression. In this Perspective, we review the origins of burst-suppression patterns and use recent insights to weigh evidence in the controversy regarding the extent to which burst-suppression patterns observed during profound anesthetic-induced brain inactivation are associated with adverse clinical outcomes. Whether the clinical intent is to avoid or maintain the brain in a state producing burst-suppression patterns, monitoring and controlling neural activity presents a technical challenge. We discuss recent advances that enable monitoring and control of burst suppression.