Creativity, that is the creation of ideas or objects considered both novel and valuable, is among the most important and highly valued of human traits, and a fundamental aspect of the sciences. Dreams and hypnagogic states have been highly influential in promoting scientific creativity and insight, contributing to some important scientific breakthroughs. Phenomenologically, the latter states of consciousness share a great deal of overlap with the psychedelic state, which has also been associated with facilitating scientific creativity on occasion. The current article proposes that the dream, hypnagogic and psychedelic states share common features that make them conducive to supporting some aspects of scientific creativity and examines the putative underlying neurophenomenological and cognitive processes involved. In addition, some notable occurrences of scientific insights that have emerged from these types of altered states are reviewed and shared common features are presented, providing a ground for future research. The psychedelic state may have its own characteristic features making it amenable to creativity enhancement, such as brain hyperconnectivity, meta-cognitive awareness, access to a more dependable and sustained altered state experience, and potential for eliciting sustained shifts in trait openness. The contextual factors which may contribute to enhancement of scientific creativity and insight will be evaluated. While research in this area is limited, further work to elucidate how psychedelics may best contribute to scientific creativity enhancement is warranted.