Control algorithms are the most critical aspects in the successful control of civil structures subjected to earthquake and wind forces. In recent years, adaptive intelligent control algorithms are emerging as an acceptable substitute method to conventional model-based control algorithms. These algorithms mainly work on the principles of artificial intelligence (AI) and soft computing (SC) methods that make them highly efficient in controlling highly nonlinear, time-varying, and time-delayed complex civil structures. The current research probes to control algorithms, that this article set forth an inclusive state-of-the-art review of adaptive intelligent control (AIC) algorithms for vibration control of smart civil structures. First, a general introduction to adaptive intelligent control is presented along with its advantages over conventional control algorithms. Second, their classification concerning artificial intelligence and soft computing methods is provided that mainly consists of artificial neural network-based controller, brain emotional learning-based intelligent controller, replicator dynamics-based controller, multi-agent system-based controller, support vector machine-based controller, fuzzy logic control, adaptive neuro-fuzzy inference system-based controller, adaptive filters-base controller, and meta-heuristic algorithms-based hybrid controllers. Third, a brief review of these algorithms with their developments on the theory and applications is provided. Fourth, we demonstrate a summarized overview of the cited literature with a brief trend analysis is presented. Finally, this study presents an overview of these innovative AIC methods that can demonstrate future directions. The contribution of this article is the anticipation of detailed and in-depth discussion into the perspective of AI and SC-based AIC method advances that enabled practical applications in attenuating vibration response of smart civil structures. Moreover, the review demonstrates the computing advantages of AIC over conventional controllers that are important in creating the next generation of smart civil structures.