The application of composite structures as elements of machines and vehicles working under various operational conditions causes degradation and occurrence of damage. Considering that composites are often used for responsible elements, for example, parts of aircrafts and other vehicles, it is extremely important to maintain them properly and detect, localize, and identify the damage occurring during their operation in possible early stage of its development. From a great variety of nondestructive testing methods developed to date, the vibration-based methods seem to be ones of the least expensive and simultaneously effective with appropriate processing of measurement data. Over the last decades a great popularity of vibration-based structural testing has been gained by wavelet analysis due to its high sensitivity to a damage. This paper presents an overview of results of numerous researchers working in the area of vibration-based damage assessment supported by the wavelet analysis and the detailed description of the Wavelet-based Structural Damage Assessment (WavStructDamAs) Benchmark, which summarizes the author’s 5-year research in this area. The benchmark covers example problems of damage identification in various composite structures with various damage types using numerous wavelet transforms and supporting tools. The benchmark is openly available and allows performing the analysis on the example problems as well as on its own problems using available analysis tools.