The penetration of distributed generators (DGs) in the existing power system has brought some real challenges regarding the power quality and dynamic response of the power systems. To overcome the above-mentioned issues, the researchers around the world have tried and tested different control methods among which the computational intelligence (CI) based methods have been found as most effective in mitigating the power quality and transient response problems intuitively. The significance of the mentioned optimization approaches in contemporary ac Microgrid (MG) controls can be observed from the increasing number of published articles and book chapters in the recent past. However, literature related to this important subject is scattered with no comprehensive review that provides detailed insight information on this substantial development. As such, this research work provides a detailed overview of four of the most extensively used CI-based optimization techniques, namely, artificial neural network (ANN), fuzzy logic (FL), adaptive neuro-fuzzy inference system (ANFIS) and genetic algorithm (GA) as applied in ac MG controls from 42 research articles along with their basic working mechanism, merits, and limitations. Due to space and scope constraints, this study excludes the applications of swarm intelligence-based optimization methods in the studied field of research. Each of the mentioned CI algorithms is explored for three major MG control applications i.e., reactive power compensation and power quality, MPPT and MG’s voltage, frequency, and power regulation. In addition, this work provides a classification of the mentioned CI-based optimization studies based on various categories such as key study objective, optimization method applied, DGs utilized, studied MG operating mode, and considered operating conditions in order to ease the searchability and selectivity of the articles for the readers. Hence, it is envisaged that this comprehensive review will provide a valuable one-stop source of knowledge to the researchers working in the field of CI-based ac MG control architectures.