Delirium is a common and severe neuropsychiatric syndrome of brain dysfunction characterized by acute and fluctuating inattention and other cognitive and perceptual deficits precipitated by acute illness. Despite being first described by Hippocrates more than two thousand years ago, there exists considerable uncertainty regarding the diagnosis of delirium due to our limited understanding of fundamental concepts, including its definition and pathophysiology. The ensuing lack of standardization results in delirium being frequently undiagnosed and significant misclassification bias in existing research. This chapter discusses the descriptive epidemiology of delirium, including methodological issues around case ascertainment in different population and clinical settings. There remains a lack of epidemiological research in the field, but we indicate the potential for observational longitudinal studies to address key questions on the population impact of delirium alongside fundamental questions of major importance to patients and their families regarding outcomes after delirium.