In our increasingly interconnected world, Cyber-Physical Systems (CPS) play a crucial role in industries like healthcare, transportation, and manufacturing by combining physical processes with computing power. These systems, however, face many challenges, especially regarding security and system faults. Anomalies in CPS may indicate unexpected problems, from sensor malfunctions to cyber-attacks, and must be detected to prevent failures that can cause harm or disrupt services. This paper provides an overview of the different ways researchers have approached anomaly detection in CPS. We categorize and compare methods like machine learning, deep learning, mathematical models, invariant, and hybrid techniques. Our goal is to help readers understand the strengths and weaknesses of these methods and how they can be used to create safer, more reliable CPS. By identifying the gaps in current solutions, we aim to encourage future research that will make CPS more secure and adaptive in our increasingly automated world.