Cyber-Physical Systems (CPS) integrate computational elements with physical processes, creating a feedback loop where physical and cyber components interact seamlessly. These systems are vital for applications such as smart grids, autonomous vehicles, industrial automation, and healthcare. CPS enhances efficiency, precision, and safety in critical industries but faces challenges like cybersecurity risks, interoperability issues, real-time constraints, and system complexity. The chapter explores the importance of anomaly detection in CPS for maintaining reliability, security, and functionality. It discusses traditional and advanced methods like machine learning (ML) and deep learning (DL) techniques, including supervised, unsupervised, and hybrid models. Approaches such as Support Vector Machines (SVM), Neural Networks, Autoencoders, and clustering techniques are highlighted for their role in identifying anomalies like system failures, cyberattacks, or inefficiencies. Further, the chapter emphasizes on the emerging areas like Federated Learning, Reinforcement Learning, and Explainable AI (XAI) to improve transparency and trust in ML models. Practical considerations like data quality, real-time processing, resource constraints, and scalability in implementing anomaly detection systems are also discussed.