Psilocybin is a psychedelic alkaloid produced naturally by various species of mushrooms, especially the genus Psilocybe, whose use by the pre-Columbian cultures has been widely documented. In the last decade, after years of stigmatization and restriction of use, research has been reactivated on the therapeutic potential of this classic psychedelic alkaloid for the treatment of multiple psychiatric disorders, including the major depressive disorder. Depression is a mood disorder whose worldwide prevalence has increased considerably in recent years and whose treatment with conventional drugs has limited effectiveness. Recent findings indicate that psilocybin, in contrast, may have a rapid and sustained antidepressant effect, even in individuals with treatment-resistant depression. Although the mechanisms underlying this effect have not yet been completely elucidated, it has been suggested that it would be mediated by changes at the level of neurotransmission, structural and functional plasticity, and connectivity of different brain networks. This narrative review presents a synthesis of the clinical evidence in favor of the antidepressant effect of psilocybin, exposes some plausible mechanisms of action that have been studied, and discusses some questions and perspectives on the use of the alkaloid in the clinical setting.