Optical elastography, the use of optics to characterize and map the mechanical properties of biological tissue, involves measuring the deformation of tissue in response to a load. Such measurements may be used to form an image of a mechanical property, often elastic modulus, with the resulting mechanical contrast complementary to the more familiar optical contrast. Optical elastography is experiencing new impetus in response to developments in the closely related fields of cell mechanics and medical imaging, aided by advances in photonics technology, and through probing the microscale between that of cells and whole tissues. Two techniques — optical coherence elastography and Brillouin microscopy — have recently shown particular promise for medical applications, such as in ophthalmology and oncology, and as new techniques in cell mechanics.