Organoids are complex multicellular three-dimensional (3D) in vitro models that are designed to allow accurate studies of the molecular processes and pathologies of human organs. Organoids can be derived from a variety of cell types, such as human primary progenitor cells, pluripotent stem cells, or tumor-derived cells and can be co-cultured with immune or microbial cells to further mimic the tissue niche. Here, we focus on the development of 3D lung organoids and their use as disease models and drug screening tools. We introduce the various experimental approaches used to model complex human diseases and analyze their advantages and disadvantages. We also discuss validation of the organoids and their physiological relevance to the study of lung diseases. Furthermore, we summarize the current use of lung organoids as models of host-pathogen interactions and human lung diseases such as cystic fibrosis, chronic obstructive pulmonary disease, or SARS-CoV-2 infection. Moreover, we discuss the use of lung organoids derived from tumor cells as lung cancer models and their application in personalized cancer medicine research. Finally, we outline the future of research in the field of human induced pluripotent stem cell-derived organoids.