Islanded microgrids (IMGs) provide a promising solution for reliable and environmentally friendly energy supply to remote areas and off-grid systems. However, the operation management of IMGs is a complex task including the coordination of a variety of distributed energy resources and loads with an intermittent nature in an efficient, stable, reliable, robust, resilient, and self-sufficient manner. In this regard, the energy management system (EMS) of IMGs has been attracting considerable attention during the last years, especially from the economic and emissions point of view. This paper provides an in-depth overview of the EMS optimization problem of IMGs by systematically analyzing the most representative studies. According to the state-of-the-art, the optimization of energy management of IMGs has six main aspects, including framework, time-frame, uncertainty handling approach, optimizer, objective function, and constraints. Each of these aspects is discussed in detail and an up-to-date overview of the existing EMSs for IMGs and future trends is provided. The future trends include the need for improved models, advanced data analytic and forecasting techniques, performance assessment of real-time EMSs in the whole MG’s control hierarchy, fully effective decentralized EMSs, improved communication and cyber security systems, and validations under real conditions. Besides, a comprehensive overview of the widely-used heuristic optimization methods and their application in EMSs of IMGs as well as their advantages and disadvantages are given. It is hoped that this study presents a solid starting point for future researches to improve the EMS of IMGs.