The growing demand and diversity in the application of industrial composites and the current inability of present non-destructive evaluation (NDE) methods to perform detailed inspection of these composites has motivated this comprehensive review of sensing technologies. NDE has the potential to be a versatile tool for maintaining composite structures deployed in hazardous and inaccessible areas, such as offshore wind farms and nuclear power plants. Therefore, the future composite solutions need to take into consideration the niche requirements of these high-value/critical applications. Composite materials are intrinsically complex due to their anisotropic and non-homogeneous characteristics. This presents a significant challenge for evaluation and the associated data analysis for NDEs. For example, the quality assurance, certification of composite structures, and early detection of the failure is complex due to the variability and tolerances involved in the composite manufacturing. Adapting existing NDE methods to detect and locate the defects at multiple length scales in the complex materials represents a significant challenge, resulting in a delayed and incorrect diagnosis of the structural health. This paper presents a comprehensive review of the NDE techniques, that includes a detailed discussion of their working principles, setup, advantages, limitations, and usage level for the structural composites. A comparison between these techniques is also presented, providing an insight into the future trends for composites’ prognostic and health management (PHM). Current research trends show the emergence of the non-contact-type NDE (including digital image correlation, infrared tomography, as well as disruptive frequency-modulated continuous wave techniques) for structural composites, and the reasons for their choice over the most popular contact-type (ultrasonic, acoustic, and piezoelectric testing) NDE methods is also discussed. The analysis of this new sensing modality for composites’ is presented within the context of the state-of-the-art and projected future requirements.