Perception is not the passive registration of incoming sensory data. Rather, it involves some analysis by synthesis, based on past experiences and context. One adaptive consequence of this arrangement is imagination-the ability to richly simulate sensory experiences, interrogate and manipulate those simulations, in service of action and decision making. In this paper, we will discuss one possible cost of this adaptation, namely hallucinations-perceptions without sensory stimulation, which characterize serious mental illnesses like schizophrenia, but which also occur in neurological illnesses, and-crucially for the present piece-are common also in the non-treatment-seeking population. We will draw upon a framework for imagination that distinguishes voluntary from non-voluntary experiences and explore the extent to which the varieties and features of hallucinations map onto this distinction, with a focus on auditory-verbal hallucinations (AVHs)-colloquially, hearing voices. We will propose that sense of agency for the act of imagining is key to meaningfully dissecting different forms and features of AVHs, and we will outline the neural, cognitive and phenomenological sequelae of this sense. We will conclude that a compelling unifying framework for action, perception and belief-predictive processing-can incorporate observations regarding sense of agency, imagination and hallucination. This article is part of the theme issue 'Offline perception: voluntary and spontaneous perceptual experiences without matching external stimulation'.