In this paper, we report a detailed overview of non-destructive techniques, specifically Acoustic emission, for structural health monitoring in engineering applications. The review comprehensively covers the application of the AE technique for data related to damping and attenuation of structural components made from various material types, including conventional and non-conventional materials. Also, this paper systematically emphasizes research related to data collection processes of variable structural elements, such as stress concentration areas, sensor placement, and methodological monitoring. In addition, the analysis discussed in the review encompasses research that has utilized the AE method to examine the performance of metal and concrete building elements in risky situations, such as high temperatures and creep factors, with and without any visible signs of damage. We also examine various solution techniques, such as empirical wavelet transforms, finite element solutions, and differential quadrature for conventional materials’ damage analysis. Furthermore, the review emphasizes using waveform schemes to assess the vulnerability of damages in unconventional materials, such as laminated composite structures with different geometrical shapes. The paper concludes by presenting an overview of the current state of the AE technique in structural health monitoring and discusses potential future developments. This review is a valuable reference for professionals and researchers engaged in engineering applications related to structural health monitoring.