Recent advances in the isolation of tissue-resident adult stem cells and the identification of inductive factors that efficiently direct differentiation of human pluripotent stem cells along specific lineages have facilitated the development of high-fidelity modelling of several tissuesin vitro. Many of the novel approaches have employed self-organizing three-dimensional (3D) culturing of organoids, which offer several advantages over conventional two-dimensional platforms. Organoid technologies hold great promise for modelling diseases and predicting the outcome of drug responsesin vitro. Here, we outline the historical background and some of the recent advances in the field of three-dimensional organoids. We also highlight some of the current limitations of these systems and discuss potential avenues to further benefit biological research using three-dimensional modelling technologies.This article is part of the theme issue ‘Designer human tissue: coming to a lab near you’.