In recent years, one of the most important issues for public security is “Automated analysis of a crowd behavior” using surveillance videos. Vision-based crowd behavior analysis methods can be divided into three categories, namely, people counting, people tracking and identification of crowd anomalies. The deployment of such an automatic system is very complex since it requires complex algorithms to detect context-sensitive uncommon behaviors of people. With this perception, we have presented an extensive review of the different methods for crowd counting, crowd tracking, and crowd anomaly detection along with the advantages and challenges associated with crowd behavior techniques. Based on the feature descriptors used to analyze the behavior of the crowd, different methods are sub-categorized into traditional feature descriptor based approaches which use handcrafted features like PCA, HOG, SIFT, optical flow, GMM, spatiotemporal filter, etc. and the self-learned feature descriptor based approaches which use deep learning models like CNN, RNN, GD-GAN, etc. Besides, in this paper, we have also presented the performance of different methods on different datasets in each class along with details of implementation. The reviews are helpful for various applications related to human activity analysis, which mainly includes crowd behavior. The methods described here can be useful in different applications of crowd behavior, For example, anomaly detection at public places. Moreover, the review helps the beginners and developers as the benchmark and the researchers of this domain to study the challenges of the crowd behavior techniques, analyze the research gap and further enhancement in these techniques.