This chapter discusses the general topic of anomaly detection and fault diagnosis. Anomaly detection techniques are supposed to identify anomalies from loads of seemingly homogeneous data and lead analysts and decision makers to timely, pivotal and actionable information. The complexity in defining anomalies translates to the challenges faced in anomaly detection. The subtle difference between change detection and anomaly detection lies in the different types of changes or anomalies to be detected. In the mission of anomaly detection, the desire to have a higher detection capability, or equivalently, a smaller type-II error, often triumphs a small type-I error. A useful pre-screening tool, as the current anomaly detection offers, is valuable in filling the void, while analysts strive for the ultimate, full automation goal. One immediate benefit of anomaly detection is that the outcomes of the detection can be used to convert the original unsupervised learning problem into a supervised learning problem.