Composite structures and materials have seen significant advancements in cost-effectiveness, product efficiency, and specific properties, leading to their extensive use in the aerospace industry. Reliable nondestructive testing (NDT) of composites is crucial for reducing maintenance costs and addressing safety concerns. This review provides a comprehensive analysis of various NDT methods, including Ultrasonic Testing, Acoustic Emission, Eddy Current Testing, Shearographic Testing, Infra-Red Thermography, and X-Ray Radiography. Each method’s principles, instruments, and applications for defect detection and damage evaluation in composite materials are thoroughly examined. The paper highlights the strengths and limitations of these NDT techniques, emphasizing their roles in ensuring the structural integrity of aerospace composites. Ultrasonic Testing and Infra-Red Thermography are identified as flexible and cost-effective solutions, widely applied in both academic research and industrial sectors. Despite the challenges in providing a complete diagnostic of structural integrity, each NDT method offers unique advantages. Future research in NDT for composites will focus on integrating advanced data processing techniques, such as machine learning and deep learning, and developing smart inspection systems with high precision and rapid data processing capabilities.