The wide range of elastic tissue properties and the difference in elasticity of tumors and the adjacent tissues have provided motivation for developing elasticity imaging techniques. These research efforts have converged with the development of a new imaging modality, the so-called elastography, with the acquired and processed images referred to as elastograms. This modality was pioneered for ultrasonic imaging, which provides the majority of experience on this topic. MR-elastography has been developed in recent years. The published clinical data range from the characterization of prostate and breast cancer in oncology and dynamic examinations of skeletal muscle to intravascular elastic differentiation of vessel plaques. Advantages of the ultrasonic elastography are ubiquitous applicability and cost-effectiveness. MR elastography offers improved reconstruction and the possibility to assess potential anisotropic properties. The different approaches of elastography, their technical and clinical application and the limitations known so far are reviewed in this paper.