Automated crowd anomaly detection and crowd scene analysis is a novel and emerging field of computer science and engineering domain. The analysis of crowd behavior based on density, trajectory, and motion helps prevent abnormal and unwanted incidents. The analysis of crowd behavior is complex and challenging due to visual occlusions, clutter, ambiguities, dense crowd, and scene semantics. These days, researchers are focusing on developing machine learning-based approaches for “crowd behavior, activity analysis, motion pattering, and anomaly detection in real-time applications”. Firstly this study presents insight on crowd anomaly detection, ways to achieve it, and its applications and importance today. Secondly, it presents a detailed analysis of conventional machine learning as well as deep learning approaches for serving the purpose based on features, methods, datasets, and shortcomings. Thirdly it presents a thorough analysis of datasets and performance parameters. Finally, it presents the current challenges and future work in this field.