This paper presents the updated status of energy storage (ES) technologies, and their technical and economical characteristics, so that, the best technology can be selected either for grid-connected or off-grid power system applications. Considering the wide range of applications, effective ways of storing and retrieving electrical energy remains a challenge. In addition to load variations, the ever-increasing penetration of intermittent renewable energies into the power system has presented the system with difficulties. Frequency regulation, voltage support, load leveling, peak shaving, economic dispatch, and production leveling represent the main power system applications, where ES can play an important role. In off-grid applications, ES can be used to balance the generation and consumption, to prevent frequency and voltage deviations. Due to the widespread use of battery energy storage (BES), the paper further presents various battery models, for power system economic analysis, reliability evaluation, and dynamic studies.