The recent renaissance of psychedelic science has reignited interest in the similarity of drug-induced experiences to those more commonly observed in psychiatric contexts such as the schizophrenia spectrum. This report from a multidisciplinary working group of the International Consortium on Hallucinations Research (ICHR) addresses this issue, putting special emphasis on hallucinatory experiences. We review evidence collected at different scales of understanding, from pharmacology to brain-imaging, phenomenology and anthropology, highlighting similarities and differences between hallucinations under psychedelics and in the schizophrenia-spectrum disorders. Finally, we attempt to integrate these findings using computational approaches and conclude with recommendations for future research.