Crow Search Algorithm (CSA) is a recent swarm intelligence optimization algorithm inspired by the social intelligent behavior of crows for hiding food. It has been widely used to solve a large variety of optimization problems in several fields and areas of research and has proved its efficiency compared to several state-of-the-art optimization algorithms available in the literature. This paper presents a comprehensive overview of Crow Search Algorithm and its new variants categorized into modified and hybridized versions. It also describes the several applications of CSA in various domains such as feature selection, image processing, scheduling, economic dispatch, distributed generation, and other engineering problems. In addition, the paper suggests some interesting research areas related to CSA enhancement, CSA hybridization, and possible new applications.