Anecdotal evidence has indicated that psychedelic substances may acutely enhance creative task performance, although empirical support for this claim is mixed at best. Clinical research has shown that psychedelics might have enduring effects on mood and well-being. However, there is no neurocognitive framework that ties acute changes in cognition to long-term effects in mood. In this review, we operationalize creativity within an emerging cognitive control framework and assess the current empirical evidence of the effects of psychedelics on creativity. Next, we leverage insights about the mechanisms and computations by which other psychoactive drugs act to enhance versus impair cognition, in particular to those that act on catecholamines, the neurophysiological consequences of which are relatively well understood. Finally, we use the same framework to link the suggested psychedelic-induced improvements in creativity with enduring psychedelic-induced improvements in mood.