The increasing penetration of Microgrids (MGs) into existing power systems and ''plug and play'' capability of Distributed Generators (DGs) causes large overshoots and settling times along with various power quality issues such as voltage and frequency flickers, current harmonics and short current transients. In this context, over the past few years, considerable research has been undertaken to investigate and address the mentioned issues using different control schemes in conjunction with soft computational techniques. The recent trends and advancements in the field of Artificial Intelligence (AI) have led the development of Swarm Intelligence (SI) based optimized controllers for smooth Renewable Energy Sources (RES) penetration and optimal voltage, frequency, and power-sharing regulation. Moreover, the recent studies have proved that the SI-based controllers provide enhanced dynamic response, optimized power quality and improved the dynamic stability of the MG systems as compared to the conventional control methods. Their importance in modern AC MG architectures can be judged from the growing number of publications in the recent past. However, literature, pertaining to SI applications to AC MG, is scattered with no comprehensive review on this significant development. As such, this study provides an overview of 15 different SI optimization techniques as applied to AC MG controls from 43 research publications including a detailed review of one of the elementary and most widely used SI based metaheuristic optimization algorithms called Particle Swarm Optimization (PSO) algorithm. This comprehensive review provides a valuable one-stop source of knowledge for the researchers and experts working on SI controller's applications for AC MG dynamic response and power quality improvements.