This study presents a comprehensive review of the history of research and development of different damage-detection methods in the realm of composite structures. Different fields of engineering, such as mechanical, architectural, civil, and aerospace engineering, benefit excellent mechanical properties of composite materials. Due to their heterogeneous nature, composite materials can suffer from several complex nonlinear damage modes, including impact damage, delamination, matrix crack, fiber breakage, and voids. Therefore, early damage detection of composite structures can help avoid catastrophic events and tragic consequences, such as airplane crashes, further demanding the development of robust structural health monitoring (SHM) algorithms. This study first reviews different non-destructive damage testing techniques, then investigates vibration-based damage-detection methods along with their respective pros and cons, and concludes with a thorough discussion of a nonlinear hybrid method termed the Vibro-Acoustic Modulation technique. Advanced signal processing, machine learning, and deep learning have been widely employed for solving damage-detection problems of composite structures. Therefore, all of these methods have been fully studied. Considering the wide use of a new generation of smart composites in different applications, a section is dedicated to these materials. At the end of this paper, some final remarks and suggestions for future work are presented
