The historical reliance of biological research on the use of animal models has sometimes made it challenging to address questions that are specific to the understanding of human biology and disease. But with the advent of human organoids - which are stem cell-derived 3D culture systems - it is now possible to re-create the architecture and physiology of human organs in remarkable detail. Human organoids provide unique opportunities for the study of human disease and complement animal models. Human organoids have been used to study infectious diseases, genetic disorders and cancers through the genetic engineering of human stem cells, as well as directly when organoids are generated from patient biopsy samples. This Review discusses the applications, advantages and disadvantages of human organoids as models of development and disease and outlines the challenges that have to be overcome for organoids to be able to substantially reduce the need for animal experiments.