This Review highlights approaches used to generate somatic cell-derived organoids for modelling epithelial tissue to understand disease progression and how they are employed in preclinical drug screening. Recent progress in our understanding of the regulation of epithelial tissue stem cells has allowed us to exploit their abilities and instruct them to self-organize into tissue-mimicking structures, so-called organoids. Organoids preserve the molecular, structural and functional characteristics of their tissues of origin, thus providing an attractive opportunity to study the biology of human tissues in health and disease. In parallel to deriving organoids from yet-uncultured epithelial tissues, the field is devoting a growing amount of effort to model human diseases using organoids. This Review describes multidisciplinary approaches for creating organoid models of human genetic, neoplastic, immunological and infectious diseases, and details how they have contributed to our understanding of disease biology. We further highlight the potential role as well as limitations of organoids in clinical practice and showcase the latest achievements and approaches for tuning the organoid culture system to position organoids in biologically defined settings and to grant organoids with better representation of human tissues.