This review describes the Hierarchical Taxonomy of Psychopathology (HiTOP) model of psychosis-related psychopathology, the psychosis superspectrum. The HiTOP psychosis superspectrum was developed to address shortcomings of traditional diagnoses for psychotic disorders and related conditions including low reliability, arbitrary boundaries between psychopathology and normality, high symptom co-occurrence, and heterogeneity within diagnostic categories. The psychosis superspectrum is a transdiagnostic dimensional model comprising two spectra—psychoticism and detachment—which are in turn broken down into fourteen narrow components, and two auxiliary domains—cognition and functional impairment. The structure of the spectra and their components are shown to parallel the genetic structure of psychosis and related traits. Psychoticism and detachment have distinct patterns of association with urbanicity, migrant and ethnic minority status, childhood adversity, and cannabis use. The superspectrum also provides a useful model for describing the emergence and course of psychosis, as components of the superspectrum are relatively stable over time. Changes in psychoticism predict the onset of psychosis-related psychopathology, whereas changes in detachment and cognition define later course. Implications of the superspectrum for genetic, socio-environmental, and longitudinal research are discussed. A companion review focuses on neurobiology, treatment response, and clinical utility of the superspectrum, and future research directions.