This review examines the essential application of non-destructive testing (NDT) techniques in assessing the integrity and damage of composite materials used in aerospace engineering, focusing on polymer matrix composites (PMCs), metal matrix composites (MMCs), and ceramic matrix composites (CMCs). As these materials increasingly replace traditional metallic and alloy components due to their advantageous properties, such as light weight, high strength, and corrosion resistance, ensuring their structural integrity becomes paramount. Here, various NDT techniques were described in detail, including ultrasonic, radiographic, and acoustic emission, among others, highlighting their significance in identifying and evaluating damages that are often invisible, yet critical, to parts safety. It stresses the need for innovation in NDT technologies to keep pace with the evolving complexity of composite materials and their applications. The review underscores the ongoing challenges and developments in NDT, advocating for enhanced techniques that provide accurate, reliable, and timely assessments to ensure the safety and durability of aerospace components. This comprehensive analysis not only illustrates current capabilities but also directs future research pathways for improving NDT methodologies in aerospace material engineering.