Microgrids are considered an adequate alternative to overcome the challenges involving integrating distributed energy resources in distribution systems to contribute to the 'Three D' trend in the electricity sector, i.e., decentralize, decarbonize, and digitize electricity. This paper reviews the most relevant works to establish a baseline for the advancement and development of smart transformer-based meshed hybrid microgrids and energy management systems. First, the structure of the solid-state transformers as smart transformers and their potential application as an energy router in a microgrid is discussed. Then, the principle of conformation of meshed hybrid microgrids based on a smart transformer and the topologies reported in the literature are reviewed. Finally, power management systems integrated into smart transformers-based meshed hybrid microgrids are studied. According to the findings and conclusions, it is considered that smart transformers-based meshed hybrid microgrids operated by an optimal energy management system under uncertainty are a potentially feasible technological alternative for the adequate penetration of distributed energy resources into local distribution systems.