Magnetic resonance elastography (MRE) is a method to estimate the mechanical properties of soft tissue from MR images of vibration-induced shear waves. In this presentation, I introduce the fundamental principles of MRE: material properties and their relationships to wave speed; how to induce waves in tissue; basic imaging sequences used in MRE; and the inversion of shear wave fields to estimate mechanical properties. Applications of MRE include the clinically important, non-invasive measurement of liver stiffness, and emerging studies of brain, breast, kidney, intervertebral disc, and muscle. New MRE methods are under development to estimate anisotropic (direction-dependent) mechanical properties in tissue.