The energy sector is undergoing a paradigm shift among all the stages, from generation to the consumer end. The affordable, flexible, secure supply−demand balance due to an increase in renewable energy sources (RESs) penetration, technological advancements in monitoring and control, and the active nature of distribution system components have led to the development of microgrid (MG) energy systems. The intermittency and uncertainty of RES, as well as the controllable nature of MG components such as different types of energy generation sources, energy storage systems, electric vehicles, heating, and cooling systems are required to deploy efficient energy management systems (EMSs). Multi-agent systems (MASs) and model predictive control (MPC) approaches have been widely used in recent studies and have characteristics that address most of the EMS challenges. The advantages of these methods are due to the independent characteristics and nature of MAS, the predictive nature of MPC, and their ability to provide affordable, flexible, and secure MG operation. Therefore, for the first time, this state-of-the-art review presents a classification of the MG control and optimization methods, their objectives, and help in understanding the MG operational and EMS challenges from the perspective of the energy trilemma (flexibility, affordability, and security). The control and optimization architectures achievable with MAS and MPC methods predominantly identified and discussed. Furthermore, future research recommendations in MG-EMS in terms of energy trilemma associated with MAS, MPC methods, stability, resiliency, scalability improvements, and algorithm developments are presented to benefit the research community.