After a 40-year hiatus, the question of whether psychedelics can increase creativity is being asked with renewed vigor. This article critically reviews the conceptual issues of studying psychedelic-induced creativity by summarizing the limited evidence on the question and suggesting two broader frameworks. There are two important challenges to researchers on this topic. One is to separate creativity from other effects of the drug that may be mistaken for creativity. The second is to develop operational measures to quantify it. This article reviews the major studies assessing creativity (or related constructs) induced by psychedelics, including a reanalysis of raw data from one study. Results are modest and inconclusive but are consistent with reports that psychedelics give rise to unusual or novel thoughts. Given the lack of robust changes in creativity measures, I suggest creativity may be too specific of a construct to accurately and fully characterize the putatively beneficial cognitive changes that psychedelic users report. Feelings of creativity may be an inconsistent result of a more general effect of these drugs, such as alterations in availability of mental representations or changes in Bayesian inference. Ultimately, creativity may not be a sufficiently creative construct to capture the beneficial effects of psychedelics.