The increasing use of the Renewable Energy Sources (RES) and the intermittency of the power generated by them create stability, reliability and power quality problems in the main electrical grid. The microgrid is called to be a feasible alternative to solve these issues. As it is a weak electrical grid, the microgrid is very sensitive to load or generation changes. To reduce the effect of these variations and to better harness the energy generated by RES, the Energy Storage Systems (ESS) are used. As the different ESS technologies that are currently available are not enough to satisfy the wide frequency spectrum of the generated energy, the use of a Hybrid Energy Storage System (HESS) is necessary. A HESS is usually formed by two complementary storage devices that can be associated in many different topologies. Of course, the two devices have to be coordinated by an Energy Management System (EMS). In this paper the different topologies and energy management algorithms that have been applied in the RES and microgrid contexts have been analysed and compared. A review of the latest papers related to the use of HESS to facilitate the integration of the RES in the microgrid context is carried out. Some examples of the (hybrid) electric vehicles are also addressed, as the use of the HESS is more extended in this field than in the field of the microgrids.