The current energy system requires fast and long-term energy storage delivery. While energy-intensive energy storage systems, like batteries or hydrogen, can provide energy in the long term (e.g., hours or days), their fast dynamic power delivery is either constrained or strongly affects their lifespan. Power-intensive energy storage systems are specific technologies developed for allowing short-term high-power energy delivery. This specific characteristic is particularly useful for compensating fast-dynamic phenomena, such as faults or voltage dips, or optimizing energy-intensive technologies’ efficiency and lifespan. This chapter describes the basic principle, operation, and network integration of the two most common power-intensive energy storage systems: the supercapacitor energy storage system (SCES) and the superconducting magnetic energy storage system (SMES). Their system hybridization with energy-intensive ESS is discussed, highlighting the control possibilities.