Over the past few decades, pulmonary imaging technologies have advanced from chest radiography and nuclear medicine methods to high-spatial-resolution or low-dose chest CT and MRI. It is currently possible to identify and measure pulmonary pathologic changes before these are obvious even to patients or depicted on conventional morphologic images. Here, key technological advances are described, including multiparametric CT image processing methods, inhaled hyperpolarized and fluorinated gas MRI, and four-dimensional free-breathing CT and MRI methods to measure regional ventilation, perfusion, gas exchange, and biomechanics. The basic anatomic and physiologic underpinnings of these pulmonary functional imaging techniques are explained. In addition, advances in image analysis and computational and artificial intelligence (machine learning) methods pertinent to functional lung imaging are discussed. The clinical applications of pulmonary functional imaging, including both the opportunities and challenges for clinical translation and deployment, will be discussed in part 2 of this review. Given the technical advances in these sophisticated imaging methods and the wealth of information they can provide, it is anticipated that pulmonary functional imaging will be increasingly used in the care of patients with lung disease. © RSNA, 2021 Online supplemental material is available for this article.