Zoonotic viruses with the ability to replicate in the human respiratory tract pose a threat to public health. Organoids, which are highly representative, multicellular models representing specific organs or tissues, can aid in our understanding of the pathogenesis, pathogenicity, transmissibility, and reservoir circulation dynamics of zoonotic viruses. Organoid studies can facilitate the rapid selection of antiviral therapies identification of potential reservoir species and intermediate hosts, and inform the selection of suitable laboratory animal models. We review the use of human- and animal-derived organoid models from multiple organs to investigate the threat of emerging zoonotic viruses that cause respiratory disease.