Microgrid concept has been widely adopted by power and energy community to boost the resilience and enhance the economics of the energy system. Stability control and economic control are two main factors to enable the reliable and efficient operation of microgrids. This paper presents two different control approaches for microgrids. The first control method adopts hierarchical structure. Each controllable resource is complied with a local controller and the microgrid is managed and optimized by a central supervisor controller. The second control method adopts the distributed structure. Distributed controller of each energy resource can communicate with each other to achieve global goals. This paper discusses the main features of these two methods and provides recommendations on how to choose appropriate control for different types of microgrids. A case study illustrates the performance difference of the two methods from economic point of view.