How do psychedelic drugs produce their characteristic range of acute effects in perception, emotion, cognition, and sense of self? How do these effects relate to the clinical efficacy of psychedelic-assisted therapies? Efforts to understand psychedelic phenomena date back more than a century in Western science. In this article I review theories of psychedelic drug effects and highlight key concepts which have endured over the last 125 years of psychedelic science. First, I describe the subjective phenomenology of acute psychedelic effects using the best available data. Next, I review late 19th-century and early 20th-century theories-model psychoses theory, filtration theory, and psychoanalytic theory-and highlight their shared features. I then briefly review recent findings on the neuropharmacology and neurophysiology of psychedelic drugs in humans. Finally, I describe recent theories of psychedelic drug effects which leverage 21st-century cognitive neuroscience frameworks-entropic brain theory, integrated information theory, and predictive processing-and point out key shared features that link back to earlier theories. I identify an abstract principle which cuts across many theories past and present: psychedelic drugs perturb universal brain processes that normally serve to constrain neural systems central to perception, emotion, cognition, and sense of self. I conclude that making an explicit effort to investigate the principles and mechanisms of psychedelic drug effects is a uniquely powerful way to iteratively develop and test unifying theories of brain function.