Psychedelic drugs, such as lysergic acid diethylamide (LSD), mescaline, and psilocybin, exert profound effects on brain and behavior. After decades of difficulties in studying these compounds, psychedelics are again being tested as potential treatments for intractable biomedical disorders. Preclinical research of psychedelics complements human neuroimaging studies and pilot clinical trials, suggesting these compounds as promising treatments for addiction, depression, anxiety, and other conditions. However, many questions regarding the mechanisms of action, safety, and efficacy of psychedelics remain. Here, we summarize recent preclinical and clinical data in this field, discuss their pharmacological mechanisms of action, and outline critical areas for future studies of psychedelic drugs, with the goal of maximizing the potential benefits of translational psychedelic biomedicine to patients. Psychedelic drugs profoundly alter human behavior, acting primarily via agonism at the 5-HT_2A receptor in the brain. Research into the mechanisms of psychedelic drugs is experiencing a renaissance after years of stagnation. Animal models show that psychedelic drugs alter a number of crucial molecular mechanisms. Psychedelic drugs cause widespread changes in cognition and brain connectivity. Recent pilot studies show LSD and psilocybin are effective in treating psychiatric disorders and possibly other illnesses. Psychedelic biomedicine is rapidly emerging as an important area of translational research.