The mobility applications of laminated composites are constantly expanding due to their improved mechanical properties and superior strength-to-weight ratio. Such advancements directly contribute to a significant reduction in energy consumption in mobile applications. However, the orthotropic nature of these materials results in complex failure modes that require advanced damage detection techniques to prevent catastrophic failures. Therefore, various non-destructive evaluation techniques for structural health monitoring (SHM) of laminated composites are constantly being developed. Moreover, due to the latest advancements in intelligent computational methods, such as machine learning and deep learning, more reliable inspections can be performed. This review discusses current advances in SHM of composite laminates for safety–critical mobility applications such as aerospace, automobile, and marine. A comprehensive overview of the steps involved in SHM of mobility composite structures, such as sensing systems and intelligent computational methods, is presented. Additionally, the review discusses the procedure for developing these intelligent computational methods. The article also describes various public-domain datasets that readers can utilize to create novel, intelligent computational methods. Finally, potential research directions are highlighted that will enable researchers and practitioners to develop more accurate and efficient damage monitoring systems for mobility composite structures.