It is a simple observation that the function of the central nervous system changes abruptly at certain critical brain concentrations of the anesthetic drug. This can be viewed as analogous to “state transitions” in systems of interacting particles, which have been extensively studied in the physical sciences. Theoretical models of the electroencephalogram (EEG) are in semi-quantitative agreement with experimental data and show some features suggestive of anesthetic-induced state transitions (critical slowing, the biphasic effect, increase in spatial correlations, and entropy changes). However, the EEG is only an indirect marker of the (unknown) networks of cortical connectivity that are required for the formation of consciousness. It is plausible that anesthetic-induced alteration in cortical and corticothalamic network topology prevents the formation of a giant component in the neuronal population network, and hence induces unconsciousness.