Classic psychedelic drugs such as psilocybin and lysergic acid diethylamide (LSD) have recaptured the imagination of both science and popular culture, and may have efficacy in treating a wide range of psychiatric disorders. Human and animal studies of psychedelic drug action in the brain have demonstrated the involvement of the serotonin 2A (5-HT2A) receptor and the cerebral cortex in acute psychedelic drug action, but different models have evolved to try to explain the impact of 5-HT2A activation on neural systems. Two prominent models of psychedelic drug action (the cortico-striatal thalamo-cortical, or CSTC, model and relaxed beliefs under psychedelics, or REBUS, model) have emphasized the role of different subcortical structures as crucial in mediating psychedelic drug effects. We describe these models and discuss gaps in knowledge, inconsistencies in the literature and extensions of both models. We then introduce a third circuit-level model involving the claustrum, a thin strip of grey matter between the insula and the external capsule that densely expresses 5-HT2A receptors (the cortico-claustro-cortical, or CCC, model). In this model, we propose that the claustrum entrains canonical cortical network states, and that psychedelic drugs disrupt 5-HT2A-mediated network coupling between the claustrum and the cortex, leading to attenuation of canonical cortical networks during psychedelic drug effects. Together, these three models may explain many phenomena of the psychedelic experience, and using this framework, future research may help to delineate the functional specificity of each circuit to the action of both serotonergic and non-serotonergic hallucinogens.