Elasticity is a material property that is closely related to the bond system of a crystal. As a consequence, the elastic stiffness is an extremely sensitive probe for detecting structural instabilities and for the investigation of certain dynamic processes. Anelastic relaxation of certain defects in the crystal, the transition from static to dynamic behavior and order/disorder processes, for example, are often associated with different elastic anomalies of the crystal. Structural instabilities, which might lead to phase transitions, in many cases manifest in characteristic elastic behavior far away from the transition temperature.