Abstract This paper introduces a comprehensive and exhaustive overview of the cuckoo search algorithm (CSA). CSA is a metaheuristic swarm-based approach established by Yang and Deb [10] to emulate the cuckoo breeding behavior. Owing to the successful application of CSA for a wide variety of optimization problems, since then, researchers have developed several new algorithms in this field. This article displays a comprehensive review of all conducting intensive research survey into the pros and cons, main architecture, and extended versions of this algorithm. It is worth mentioning that the materials of this survey paper are categorized in accordance with the structure of the CSA in which the materials are divided into the CSA versions and modification, publication years, the CSA applications areas, and the hybridization of CSA. The survey paper ends with solid conclusions about the current research on CSA and the possible future directions for the relevant audience and readers. The researchers and practitioners on CSA belong to a wide range of audiences from the domains of optimization, engineering, medical, data mining, clustering, etc., who will benefit from this study.