Microgrids have been proposed as a solution to the growing deterioration of traditional electrical power systems and the energy transition towards renewable sources. One of the most important aspects of the efficient operation of a microgrid is its topology, that is, how the components are connected. Some papers have studied microgrid topologies; however, these studies do not perform an exhaustive analysis of the types of topologies, their applications, characteristics, or technical advantages and disadvantages. The contribution of this paper is the integration of the most important functional properties of microgrid topologies in terms of reliability, efficiency, structure, costs, and control methods. The study analyzes 21 topologies divided into six classifications with their respective sub-classifications. The analysis was based on the characteristics of the current (AC or DC), the control mechanisms, the transition between the operating modes, and the operating costs. As a result of the evaluation, it was evidenced that SST-based completely isolated coupled AC topologies, completely isolated two-stage AC decoupled, and multiple microgrids show the best performances. In contrast, the use of two-stage and three-stage partially isolated AC decoupled topologies is not recommended because of their high operating cost and low efficiency and reliability.