Ultrasonography has been widely used for diagnosis since it was first introduced in clinical practice in the 1970's. Since then, new ultrasound modalities have been developed, such as Doppler imaging, which provides new information for diagnosis. Elastography was developed in the 1990's to map tissue stiffness, and reproduces/replaces the palpation performed by clinicians. In this paper, we introduce the principles of elastography and give a technical summary for the main elastography techniques: from quasi-static methods that require a static compression of the tissue to dynamic methods that uses the propagation of mechanical waves in the body. Several dynamic methods are discussed: vibro-acoustography, Acoustic Radiation Force Impulsion (ARFI), transient elastography, shear wave imaging, etc. This paper aims to help the reader at understanding the differences between the different methods of this promising imaging modality that may become a significant tool in medical imaging.