Renewable energy generation exhibits inherent volatility and randomness, which can easily lead to frequency/voltage fluctuations in power systems. Moreover, the lack of inherent inertia and active grid-support capabilities in renewable units poses significant challenges to grid stability under high renewable penetration. Owing to their rapid response and flexible control characteristics, energy storage systems can effectively enhance renewable energy accommodation and strengthen the active support capability of power grids. Focusing on grid-support applications of battery energy storage systems (BESSs), this paper systematically analyzes their technical features and functional roles. By emulating key parameters of synchronous generators (active/reactive power, inertia, and damping), a comprehensive overview of active grid support strategies enabled by BESSs is presented from the perspectives of frequency regulation and peaking shaving, voltage regulation, inertia support, and damping compensation. Aiming at the deficiencies in existing research regarding multi-type energy storage coordinated control, dynamic synergistic control, and economic and safety considerations, potential solutions encompassing theoretical innovation, technological advancement, and market mechanism innovation are proposed. It provides a theoretical foundation and technological pathways for BESSs in supporting power systems.