Background/Objectives: Neuropathic and chronic centralized pain disorders remain difficult to treat because they involve central sensitization, maladaptive neuroplasticity, neuroimmune activation, affective amplification, and large-scale network dysfunction. Psilocybin, a serotonergic psychedelic acting primarily through 5-HT2A receptor agonism, has emerged as a candidate modulator of chronic pain states; however, clinical evidence remains preliminary. This review synthesizes preclinical, clinical, and mechanistic literature on psilocybin in chronic neuropathic and centralized pain, emphasizing biological plausibility, translational gaps, and future trial design. Methods: PubMed/MEDLINE, Google Scholar, bioRxiv, medRxiv, and targeted journal searches were reviewed through February 2026 and supplemented by reference screening. Thirty-seven peer-reviewed evidence sources were retained for mechanistic synthesis, and ClinicalTrials.gov records were reviewed separately to contextualize the registered clinical-trial landscape. Evidence was synthesized narratively because heterogeneity in study design, pain models, interventions, outcomes, and follow-up precluded meta-analysis. Results: Several preclinical studies reported psilocybin-associated reductions in allodynia, hypersensitivity, formalin-induced nociception, or pain-related affective behaviors in selected rodent models, with some effects linked to 5-HT2A signaling. However, findings were not uniform, and one rigorous null study found no immediate or persistent analgesic effect across multiple models. Human evidence remains limited and is primarily derived from one small open-label fibromyalgia pilot trial, case reports or case series, and survey studies, and has been summarized in recent systematic and narrative reviews. Collectively, these data remain insufficient to establish clinical efficacy. Four putative mechanistic domains were identified: descending serotonergic modulation, 5-HT2A- and TrkB/BDNF-related neuroplasticity, neuroimmune/microglial modulation, and affective-salience/default mode network reorganization. Conclusions: Psilocybin should not currently be regarded as an established analgesic. Available evidence supports a biologically plausible but clinically unproven model requiring phenotype-specific randomized trials with active controls, biomarkers, and long-term follow-up.