Lamb waves (LWs) are guided waves (GWs) with unique properties that make them ideal for Non-Destructive Testing (NDT) and Structural Health Monitoring (SHM). Over the last two decades, LW-based techniques have gained significant traction in academic and industrial research. A primary advantage of LWs is their ability to propagate over long distances in plate or shell structures, navigating curves and reaching hidden or buried areas, capabilities essential for detecting interlaminar damage in composites. As LW wave structures are frequency and phase-velocity-dependent, they are now suitable for various engineering applications, offering a promising, cost-effective solution for automated, real-time structural integrity monitoring. This paper provides a comprehensive overview of LW behavior, modeling, applications, and limitations in detecting fatigue damage within composite structures. Furthermore, the study explores the integration of Artificial Intelligence (AI) algorithms, including Artificial Neural Networks (ANNs), Machine Learning (ML), and Deep Learning (DL), which have emerged as powerful tools for predicting fatigue damage. By leveraging historical data from LW sensing systems, these AI models can accurately forecast structural conditions without the need for complex analytical modeling, significantly reducing processing time.