Psychedelics are drugs capable of eliciting profound alterations in the subjective experience of the users, sometimes with long-lasting consequences. Because of this, psychedelic research tends to focus on human subjects, given their capacity to construct detailed narratives about the contents of their consciousness experiences. In spite of its relevance, the interaction between serotonergic psychedelics and language production is comparatively understudied in the recent literature. This review is focused on two aspects of this interaction: how the acute effects of psychedelic drugs impact on speech organization regardless of its semantic content, and how to characterize the subjective effects of psychedelic drugs by analyzing the semantic content of written retrospective reports. We show that the computational characterization of language production is an emergent powerful tool to predict the therapeutic outcome of individual experiences, relate the effects elicited by psychedelics with those associated with other altered states of consciousness, draw comparisons between the psychedelic state and the symptomatology of certain psychiatric disorders, and investigate the neurochemical profile and mechanism of action of different psychedelic drugs. We conclude that researchers studying psychedelics can considerably expand the range of their potential scientific conclusions by analyzing brief interviews obtained before, during and after the acute effects. Finally, we list a series of questions and open problems that should be addressed to further consolidate this approach.