Advances in electroencephalogram (EEG) processing have produced new interest in measuring anesthesia using the EEG. There are a number of EEG-based anesthesia ‘depth’ monitors now available and their use in pediatric anesthesia is increasing. Although these monitors have been extensively studied in adults, there are relatively few studies examining their validity or use in children. To some extent we must rely on adult data. However, extrapolation of data from adults to children requires an in depth understanding of the physiology behind the data. The first question is what is being measured. What is anesthesia? A model of anesthesia has several components with arousal as a core component. Arousal can be linked to clinical observations, and correlates with anatomical and physiological studies. The EEG has characteristics that fairly consistently change with arousal during anesthesia, but the relationship between arousal and the EEG is imprecise and drug dependent. This relationship is the basis for using the EEG to measure anesthesia and provides only an indirect measure of consciousness and memory formation. A good understanding of how the EEG is related to anesthesia is essential when interpreting the EEG during anesthesia, and especially when extending the use of the EEG to measure anesthesia in children. Physiological studies in adults and children indicate that EEG-derived anesthesia depth monitors can provide an imprecise and drug-dependent measure of arousal. Although the outputs from these monitors do not closely represent any true physiological entity, they can be used as guides for anesthesia and in so doing have improved outcomes in adults. In older children the physiology, anatomy and clinical observations indicate the performance of the monitors may be similar to that in adults, although the clinical relevance of outcomes may be different. In infants their use cannot yet be supported in theory or in practice.