An outlier is an event or observation that is defined as an unusual activity, intrusion, or a suspicious data point that lies at an irregular distance from a population. The definition of an outlier event, however, is subjective and depends on the application and the domain (Energy, Health, Wireless Network, etc.). It is important to detect outlier events as carefully as possible to avoid infrastructure failures because anomalous events can cause minor to severe damage to infrastructure. For instance, an attack on a cyber-physical system such as a microgrid may initiate voltage or frequency instability, thereby damaging a smart inverter which involves very expensive repairing. Unusual activities in microgrids can be mechanical faults, behavior changes in the system, human or instrument errors or a malicious attack. Accordingly, and due to its variability, Outlier Detection (OD) is an ever-growing research field. In this chapter, we discuss the progress of OD methods using AI techniques. For that, the fundamental concepts of each OD model are introduced via multiple categories. Broad range of OD methods are categorized into six major categories: Statistical-based, Distance-based, Density-based, Clustering-based, Learning-based, and Ensemble methods. For every category, we discuss recent state-of-the-art approaches, their application areas, and performances. After that, a brief discussion regarding the advantages, disadvantages, and challenges of each technique is provided with recommendations on future research directions. This survey aims to guide the reader to better understand recent progress of OD methods for the assurance of AI.