Elastography or elasticity imaging can be defined as the science and methodology of estimating the mechanical properties of a medium (including soft tissue). Elastography methods generally use an external source of force to produce a static or dynamic stress distribution on the probed medium. The applied stress causes a displacement distribution within the medium, which can be measured or imaged by ultrasound, magnetic resonance, or optical methods. In this paper, the relation of elastography to tissue pathology will be described and an overview of a number of recent patents will be provided. The most representative patents on both static and dynamic elastography methods will be presented, and emphasis will be given on the dynamic-based methods and devices that rely on the acoustic radiation force of ultrasound. A short reference will be also provided to patents on magnetic resonance elastography.