Pulmonary functional magnetic resonance imaging (PfMRI) provides a way to non-invasively map and measure the spatial distribution of pulmonary ventilation, perfusion and gas-exchange abnormalities with unprecedented detail of functional processes at the level of airways, alveoli and the alveolar-capillary membrane. Current PfMRI approaches are dominated by hyperpolarized helium-3 (3He) and xenon-129 (129Xe) gases, which both provide rapid (8-15s) and well-tolerated imaging examinations in patients with severe pulmonary diseases and pediatric populations, whilst employing no ionizing radiation. While a number of review papers summarize the required image acquisition hardware and software requirements needed to enable PfMRI, here we focus on the image analysis and processing methods required for reproducible measurements using hyperpolarized gas ventilation MRI. We start with the transition in the literature from qualitative and subjective scoring systems to quantitative and objective measurements which enable precise quantification of the lung’s critical structure-function relationships. We provide an overview of quantitative biomarkers and the relevant respiratory system parameters that may be measured using PfMRI methods, outlining the history of developments in the field, current methods and then knowledge gaps and typical limitations. We focus on hyperpolarized noble gas MR image processing methods used for quantifying ventilation and gas distribution in the lungs, and discuss the utility and applications of imaging biomarkers generated through these techniques. We conclude with a summary of the current and future directions to further the development of image processing methods, and discuss the remaining challenges for potential clinical translation of these approaches and their integration into standard clinical workflows.