Clinical studies suggest the therapeutic potential of psychedelics, including ayahuasca, DMT, psilocybin, and LSD, in stress-related disorders. These substances induce cognitive, antidepressant, anxiolytic, and antiaddictive effects suggested to arise from biological changes similar to conventional antidepressants or the rapid-acting substance ketamine. The proposed route is by inducing brain neuroplasticity. This review attempts to summarize the evidence that psychedelics induce neuroplasticity by focusing on psychedelics’ cellular and molecular neuroplasticity effects after single and repeated administration. When behavioral parameters are encountered in the selected studies, the biological pathways will be linked to the behavioral effects. Additionally, knowledge gaps in the underlying biology of clinical outcomes of psychedelics are highlighted. The literature searched yielded 344 results. Title and abstract screening reduced the sample to 35; eight were included from other sources, and full-text screening resulted in the final selection of 16 preclinical and four clinical studies. Studies (n = 20) show that a single administration of a psychedelic produces rapid changes in plasticity mechanisms on a molecular, neuronal, synaptic, and dendritic level. The expression of plasticity-related genes and proteins, including Brain-Derived Neurotrophic Factor (BDNF), is changed after a single administration of psychedelics, resulting in changed neuroplasticity. The latter included more dendritic complexity, which outlasted the acute effects of the psychedelic. Repeated administration of a psychedelic directly stimulated neurogenesis and increased BDNF mRNA levels up to a month after treatment. Findings from the current review demonstrate that psychedelics induce molecular and cellular adaptations related to neuroplasticity and suggest those run parallel to the clinical effects of psychedelics, potentially underlying them. Future (pre)clinical research might focus on deciphering the specific cellular mechanism activated by different psychedelics and related to long-term clinical and biological effects to increase our understanding of the therapeutic potential of these compounds.