The number of 5G base stations (BSs) has soared in recent years due to the exponential growth in demand for high data rate mobile communication traffic from various intelligent terminals. The 5G BSs powered by microgrids with energy storage and renewable generation can significantly reduce the carbon emissions and operational costs. The base station microgrid energy management system (BSMGEMS) is crucial to unleash these potentials. This paper presents a brief review of BSMGEMS. The work begins with outlining the main components and energy consumptions of 5G BSs, introducing the configuration and components of base station microgrids (BSMGs), as well as categorizing the energy management systems (EMSs) and communication network topology. Subsequently, the dispatch optimization strategy and energy trading models are reviewed. The paper concludes with a few suggestions for future research.