Considering the high sensitivity of the nonlinear ultrasonic measurement technique and great advantages of the guided wave testing method,the use of nonlinear ultrasonic guided waves provides a promising means for evaluating and characterizing the hidden and/or inaccessible damage/degradation in solid media.Increasing attention on the development of the testing method based on nonlinear ultrasonic guided waves is largely attributed to the theoretical advances of nonlinear guided waves propagation in solid media.One of the typical acoustic nonlinear responses is the generation of second harmonics that can be used to effectively evaluate damage/degradation in materials/structures.In this paper,the theoretical progress of second-harmonic generation (SHG) of ultrasonic guided wave propagation in solid media is reviewed.The advances and developments of theoretical investigations on the effect of SHG of ultrasonic guided wave propagation in different structures are addressed.Some obscure understandings and the ideas in dispute are also discussed.