Within the broad field of human perception lies the category of stimulus-independent perceptions, which draws together experiences such as hallucinations, mental imagery and dreams. Traditional divisions between medical and psychological sciences have contributed to these experiences being investigated separately. This review aims to examine their similarities and differences at the levels of phenomenology and underlying brain function and thus reassemble them within a common framework. Using Edmund Parish's historical work as a guiding tool and the latest research findings in the cognitive, clinical and computational sciences, we consider how different perspectives may be reconciled and help generate novel hypotheses for future research. This article is part of the theme issue ‘Offline perception: voluntary and spontaneous perceptual experiences without matching external stimulation’.