Hyperpolarized gases have found a steadily increasing range of applications in nuclear magnetic resonance (NMR) and NMR imaging (MRI). They can be regarded as a new class of MR contrast agent or as a way of greatly enhancing the temporal resolution of the measurement of processes relevant to areas as diverse as materials science and biomedicine. We concentrate on the properties and applications of hyperpolarized xenon. This review discusses the physics of producing hyperpolarization, the NMR-relevant properties of 129 Xe, specific MRI methods for hyperpolarized gases, applications of xenon to biology and medicine, polarization transfer to other nuclear species and low-field imaging.