In addition to producing profound subjective effects following acute administration, psychedelic compounds can induce beneficial behavioral changes relevant to the treatment of neuropsychiatric disorders that last long after the compounds have been cleared from the body. One hypothesis with the potential to explain the remarkable enduring effects of psychedelics is related to their abilities to promote structural and functional neuroplasticity in the prefrontal cortex (PFC). A hallmark of many stress-related neuropsychiatric diseases, including depression, post-traumatic stress disorder (PTSD), and addiction, is the atrophy of neurons in the PFC. Psychedelics appear to be particularly effective catalysts for the growth of these key neurons, ultimately leading to restoration of synaptic connectivity in this critical brain region. Furthermore, evidence suggests that the hallucinogenic effects of psychedelics are not directly linked to their ability to promote structural and functional neuroplasticity. If we are to develop improved alternatives to psychedelics for treating neuropsychiatric diseases, we must fully characterize the molecular mechanisms that give rise to psychedelic-induced neuroplasticity. Here, I review our current understanding of the biochemical signaling pathways activated by psychedelics and related neuroplasticity-promoting molecules, with an emphasis on key unanswered questions.