Objective: This study aims to provide an overview of pharmacological trials that examine the neurocognitive effects of psychedelics among healthy individuals and patients with post-traumatic stress disorder (PTSD) or major depressive disorder (MDD). Methods: The Preferred Reporting Items for Systematic Reviews (PRISMA) was used as a guide to structure and report the findings for this review. A literature search included the MEDLINE database up until December 2022. We included randomized or open-label human studies of MDMA, psilocybin, mescaline, LSD, DMT, or cannabis reporting non-emotionally charged neurocognitive outcomes (“cold cognition”) measured through validated neuropsychological tests. Results: A total of 43 full-text papers on MDMA (15), cannabis (12), LSD (6), psilocybin (9), DMT/ayahuasca (1), and mescaline (0) were included, mostly on healthy subjects. A single article on MDMA’s effects on cognition in subjects with PTSD was included; there were no studies on psychedelics and neurocognition in MDD. Most of the studies on healthy subjects reported detrimental or neutral effects on cognition during the peak effect of psychedelics with a few exceptions (e.g., MDMA improved psychomotor function). Performance on the type of neurocognitive dimension (e.g., attention, memory, executive function, psychomotor) varies by type of psychedelic, dosage, and cognitive testing. Conclusions: Small samples and a lack of uniformed methods across studies preclude unequivocal conclusions on whether psychedelics enhance, decrease, or have no significant effect on cognitive performance. It is foreseen that psychedelics will soon become an available treatment for various psychiatric disorders. The acute and long-term effects on cognition caused by psychedelics should be assessed in future studies.