One of the most obvious manifestations of the nonlinear stress-strain relation in elastic solids is the existence of thermal expansion due to a non-parabolic atomic potential. From the acoustic point of view, this nonlinearity immediately explains a variety of observations such as stress effects on the sound propagation velocities and acoustic harmonic generation, which is basically a distortion of the wave. Additional nonlinearities come about due to dislocation motion, or the initiation of plastic flow, and the nucleation of a new phase, such as in the case of a martensitic transformation, e.g. Other examples are nonlinear acoustic effects that are induced at free and internal surfaces caused for a variety of reasons. Detailed acoustic experiments on these phenomena have been made over the past forty years but the ideas have not been applied seriously in NDE. The present paper is a short review of work, some of which this author has been involved in. The objective is to show the utility of nonlinear acoustics for NDE of structural materials.