In the past decade, hyperpolarized (HP) contrast agents have been under active development for MRI applications to address the twin challenges of functional and quantitative imaging. Both HP helium (3He) and xenon (129Xe) gases have reached the stage where they are under study in clinical research. HP 129Xe, in particular, is poised for larger scale clinical research to investigate asthma, chronic obstructive pulmonary disease, and fibrotic lung diseases. With advances in polarizer technology and unique capabilities for imaging of 129Xe gas exchange into lung tissue and blood, HP 129Xe MRI is attracting new attention. In parallel, HP 13C and 15N MRI methods have steadily advanced in a wide range of pre-clinical research applications for imaging metabolism in various cancers and cardiac disease. The HP [1-13C] pyruvate MRI technique, in particular, has undergone phase I trials in prostate cancer and is poised for investigational new drug trials at multiple institutions in cancer and cardiac applications. This review treats the methodology behind both HP gases and HP 13C and 15N liquid state agents. Gas and liquid phase HP agents share similar technologies for achieving non-equilibrium polarization outside the field of the MRI scanner, strategies for image data acquisition, and translational challenges in moving from pre-clinical to clinical research. To cover the wide array of methods and applications, this review is organized by numerical section into 1) a brief introduction, 2) the physical and biological properties of the most common polarized agents with a brief summary of applications and methods of polarization, 3) methods for image acquisition and reconstruction specific to improving data acquisition efficiency for HP MRI, 4) the main physical properties that enable unique measures of physiology or metabolic pathways, followed by a more detailed review of the literature describing the use of HP agents to study 5) metabolic pathways in cancer and cardiac disease and 6) lung function in both pre-clinical and clinical research studies, 7) some future directions and challenges, and 8) an overall summary.