Abstract The hybrid AC/DC microgrids have become considerably popular as they are reliable, accessible and robust. They are utilized for solving environmental, economic, operational and power-related political issues. Having this increased necessity taken into consideration, this paper performs a comprehensive review of the fundamentals of hybrid AC/DC microgrids and describes their components. Mathematical models and valid comparisons among different renewable energy sources’ generations are discussed. Subsequently, various operational zones, control and optimization methods, power flow calculations in the presence of uncertainties related to renewable energy sources are reviewed.