Organoids have become a prominent model system in pulmonary research. The ability to establish organoid cultures directly from patient tissue has expanded the repertoire of physiologically relevant preclinical model systems. In addition to their derivation from adult lung stem/progenitor cells, lung organoids can be derived from fetal tissue or induced pluripotent stem cells to fill a critical gap in modelling pulmonary development in vitro. Recent years have seen important progress in the characterisation and refinement of organoid culture systems. Here, we address several open questions in the field, including how closely organoids recapitulate the tissue of origin, how well organoids recapitulate patient cohorts, and how well organoids capture diversity within a patient. We advocate deeper characterisation of models using single cell technologies, generation of more diverse organoid biobanks and further standardisation of culture media.