Hyperpolarization is a technique that can increase nuclear spin polarization with the corresponding gains in nuclear magnetic resonance (NMR) signals by 4–8 orders of magnitude. When this process is applied to biologically relevant samples, the hyperpolarized molecules can be used as exogenous magnetic resonance imaging (MRI) contrast agents. A technique called spin‐exchange optical pumping (SEOP) can be applied to hyperpolarize noble gases such as 129Xe. Techniques based on hyperpolarized 129Xe are poised to revolutionize clinical lung imaging, offering a non‐ionizing, high‐contrast alternative to computed tomography (CT) imaging and conventional proton MRI. Moreover, CT and conventional proton MRI report on lung tissue structure but provide little functional information. On the other hand, when a subject breathes hyperpolarized 129Xe gas, functional lung images reporting on lung ventilation, perfusion and diffusion with 3D readout can be obtained in seconds. In this Review, the physics of SEOP is discussed and the different production modalities are explained in the context of their clinical application. We also briefly compare SEOP to other hyperpolarization methods and conclude this paper with the outlook for biomedical applications of hyperpolarized 129Xe to lung imaging and beyond.