In this paper, a comprehensive overview of the Crow Search Algorithm (CSA) is introduced with detailed discussions, which is intended to keep researchers interested in swarm intelligence algorithms and optimization problems. CSA is a new swarm intelligence algorithm recently developed, which simulates crow behavior in storing excess food and retrieving it when needed. In the optimization theory, the crow is the searcher, the surrounding environment is the search space, and randomly storing the location of food is a feasible solution. Among all food locations, the location where the most food is stored is considered to be the global optimal solution, and the objective function is the amount of food. By simulating the intelligent behavior of crows, CSA tries to find optimal solutions to various optimization problems. It has gained a considerable interest worldwide since its advantages like simple implementation, a few numbers of parameters, flexibility, etc. This survey introduces a comprehensive variant of CSA, including hybrid, modified, and multi-objective versions. Furthermore, based on the analyzed papers published in the literature by some publishers such as IEEE, Elsevier, and Springer, the comprehensive application scenarios of CSA such as power, computer science, machine learning, civil engineering have also been reviewed. Finally, the advantages and disadvantages of CSA have been discussed by conducting some comparative experiments with other similar published peers.