Supercapacitors (SCs) have high power density and exceptional durability. Progress has been made in their materials and chemistries, while extensive research has been carried out to address challenges of SC management. The potential engineering applications of SCs are being continually explored. This paper presents a review of SC modeling, state estimation, and industrial applications reported in the literature, with the overarching goal to summarize recent research progress and stimulate innovative thoughts for SC control/management. For SC modeling, the state-of-the-art models for electrical, self-discharge, and thermal behaviors are systematically reviewed, where electrochemical, equivalent circuit, intelligent, and fractional-order models for electrical behavior simulation are highlighted. For SC state estimation, methods for State-of-Charge (SOC) estimation and State-of-Health (SOH) monitoring are covered, together with an underlying analysis of aging mechanism and its influencing factors. Finally, a wide range of potential SC applications is summarized. Particularly, co-working with high energy-density devices constitutes hybrid energy storage for renewable energy systems and electric vehicles (EVs), sufficiently reaping synergistic benefits of multiple energy-storage units.