Why do animals and humans do anything at all? Arousal is the most powerful and essential function of the brain, a continuous function that accounts for the ability of animals and humans to respond to stimuli in the environment by producing muscular responses. Following decades of psychological, neurophysiological and molecular investigations, generalized CNS arousal can now be analyzed using approaches usually applied to physical systems. The concept of “criticality” is a state that illustrates an advantage for arousal systems poised near a phase transition. This property provides speed and sensitivity and facilitates the transition of the system into different brain states, especially as the brain crosses a phase transition from less aroused to more aroused states. In summary, concepts derived from applied mathematics of physical systems will now find their application in this area of neuroscience, the neurobiology of CNS arousal.