Surveillance cameras have recently been utilized to provide physical security services globally in diverse private and public spaces. The number of cameras has been increasing rapidly due to the need for monitoring and recording abnormal events. This process can be difficult and time-consuming when detecting anomalies using human power to monitor them for special security purposes. Abnormal events deviate from normal patterns and are considered rare. Furthermore, collecting or producing data on these rare events and modeling abnormal data are difficult. Therefore, there is a need to develop an intelligent approach to overcome this challenge. Many research studies have been conducted on detecting abnormal events using machine learning and deep learning techniques. This study focused on abnormal event detection, particularly for video surveillance applications, and included an up-to-date state-of-the-art that extends previous related works. The major objective of this survey was to examine the existing machine learning and deep learning techniques in the literature and the datasets used to detect abnormal events in surveillance videos to show their advantages and disadvantages and summarize the literature studies, highlighting the major challenges.