Psychedelic compounds have shown extraordinary potential in treating a wide range of neuropsychiatric disorders. Psilocybin, for example, has now been shown in several clinical trials to induce a rapid (within days) and persistent (3-12 months) improvement in human treatment-resistant depression and other neuropsychiatric conditions. Here we review the preclinical models and experimental approaches that have been used to study the neurobiological actions of psychedelic drugs. We further summarize the insights these studies have provided into the possible mechanisms underlying the induction of their therapeutic actions, including the receptors to which psychedelics bind and the second messenger signaling cascades that they activate. We also discuss potential biological processes that psychedelics may alter to produce the lasting amelioration of symptoms, including improvements in synaptic structure and function and suppression of inflammation. Improved mechanistic understanding of psychedelic drug actions will aid in the advancement of these promising new medicines. This article is part of the Special Issue on "National Institutes of Health Psilocybin Research Speaker Series".