Video Surveillance Systems (VSSs) are used in a wide range of applications including public safety and perimeter security. They are deployed in places such as markets, hospitals, schools, banks, shopping malls, offices, and smart cities. VSSs generate a massive amount of surveillance data, and significant research has been published on the use of machine learning algorithms to handle surveillance data. In this paper, we present an extensive overview and a thorough analysis of cutting-edge learning methods used in VSSs. Existing surveys on learning approaches in video surveillance have some drawbacks, such as a lack of in-depth analysis of the learning algorithms, omission of certain methodologies, insufficient critical evaluation, and absence of recent learning algorithms. To fill these gaps, this survey provides a thorough examination of the most recent learning algorithms for anomaly detection. A critical assessment of the algorithms including their strengths, weaknesses, and applicability as well as tailored classifications of anomaly types for different domains are provided. Our study also offers insights into the future development of learning techniques in VSS, positioning itself as a valuable resource for both researchers and practitioners in the field. Finally, we share our thoughts on what we learned and how it can help with new developments in the future.