General anesthesia has been used in the United States for more than 167 years. Now, using systems neuroscience paradigms how anesthetics act in the brain and central nervous system to create the states of general anesthesia is being understood. Propofol is one of the most widely used and the most widely studied anesthetics. When administered for general anesthesia or sedation, the electroencephalogram (EEG) under propofol shows highly structured, rhythmic activity that is strongly associated with changes in the patient's level of arousal. These highly structured oscillations lend themselves readily to mathematical descriptions using dynamical systems models. We review recent model descriptions of the commonly observed EEG patterns associated with propofol: paradoxical excitation, strong frontal alpha oscillations, anteriorization and burst suppression. Our analysis suggests that propofol's actions at GABAergic networks in the cortex, thalamus and brainstem induce profound brain dynamics that are one of the likely mechanisms through which this anesthetic induces altered arousal states from sedation to unconsciousness. Because these dynamical effects are readily observed in the EEG, the mathematical descriptions of how propofol's EEG signatures relate to its mechanisms of action in neural circuits provide anesthesiologists with a neurophysiologically based approach to monitoring the brain states of patients receiving anesthesia care.