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Sensors are a fundamental component of Structural Health Monitoring (SHM) systems. Among the different types of sensors, piezoelectric (PZT) sensors are widely used due to their desirable properties, such as dual actuation–sensing capability, high sensitivity, low cost, and suitability for real-time monitoring. In addition to proper sensors, SHM also requires effective signal processing techniques for interpreting the data acquired by the sensors. Recently, the rapid advancement of Artificial Intelligence (AI) has significantly improved the automated SHM of structures and demonstrated how effective SHM can become when combined with artificial intelligence. Thus, the use of appropriate sensors, effective signal processing techniques, and AI can significantly enhance SHM performance. Guided by these developments, this paper presents a critical review of signal processing and machine learning approaches in PZT-based SHM systems, with emphasis on engineering structures. The fundamental principles of PZT sensing and wave propagation are first outlined. Next, signal processing techniques and their importance in SHM are discussed with a focus on recent advancements in the use of AI in PZT-based SHM. This work also discusses the Hybrid frameworks that integrate signal processing with data-driven AI models which are promising directions for improving robustness and accuracy of SHM. Finally, existing key challenges such as environmental variability, sensor degradation, data scarcity, and model generalization are discussed, along with future directions including physics-informed learning, transfer learning, explainable AI, and baseline-free SHM systems.