Diseases such as idiopathic pulmonary fibrosis, chronic obstructive pulmonary disease, and bronchopulmonary dysplasia injure the gas-exchanging alveoli of the human lung. Animal studies have indicated that dysregulation of alveolar cells, including alveolar type II stem/progenitor cells, is implicated in disease pathogenesis. Due to mouse-human differences, there has been a desperate need to develop human-relevant lung models that can more closely recapitulate the human lung during homeostasis, injury repair, and disease. Here we discuss how current single-cell RNA sequencing studies have increased knowledge of the cellular and molecular composition of human lung alveoli, including the identification of molecular heterogeneity, cellular diversity, and previously unknown cell types, some of which arise specifically during disease. For functional analysis of alveolar cells, in vitro human alveolar organoids established from human pluripotent stem cells, embryonic progenitors, and adult tissue from both healthy and diseased lungs have modeled aspects of the cellular and molecular features of alveolar epithelium. Drawbacks of such systems are highlighted, along with possible solutions. Organoid-on-a-chip and ex vivo systems including precision-cut lung slices can complement organoid studies by providing further cellular and structural complexity of lung tissues, and have been shown to be invaluable models of human lung disease, while the production of acellular and synthetic scaffolds hold promise in lung transplant efforts. Further improvements to such systems will increase understanding of the underlying biology of human alveolar stem/progenitor cells, and could lead to future therapeutic or pharmacological intervention in patients suffering from end-stage lung diseases.