In this Review, we briefly describe the basic virology and pathogenesis of SARS-CoV-2, highlighting how stem cell technology and organoids can contribute to the understanding of SARS-CoV-2 cell tropisms and the mechanism of disease in the human host, supporting and clarifying findings from clinical studies in infected individuals. We summarize here the results of studies, which used these technologies to investigate SARS-CoV-2 pathogenesis in different organs. Studies with in vitro models of lung epithelia showed that alveolar epithelial type II cells, but not differentiated lung alveolar epithelial type I cells, are key targets of SARS-CoV-2, which triggers cell apoptosis and inflammation, while impairing surfactant production. Experiments with human small intestinal organoids and colonic organoids showed that the gastrointestinal tract is another relevant target for SARS-CoV-2. The virus can infect and replicate in enterocytes and cholangiocytes, inducing cell damage and inflammation. Direct viral damage was also demonstrated in in vitro models of human cardiomyocytes and choroid plexus epithelial cells. At variance, endothelial cells and neurons are poorly susceptible to viral infection, thus supporting the hypothesis that neurological symptoms and vascular damage result from the indirect effects of systemic inflammatory and immunological hyper-responses to SARS-CoV-2 infection.