Resinous materials and rubbers are elastoviscous solids. They are very deformable and possess non-linear viscous behaviors. Their creep and stress relaxation is non-linear according to the applied stresses. Cycling loading of rubbers involves self-heating temperature enhancement. This is an overview of the damping behavior of rubberlike materials, but contains some novelties concerning the application of the nonlinear hereditary theory in the case of temperature impact. Rubberlike materials are used in different devices in order to attenuate external shock impacts, in the case of seismic protection and in automotive tire production.