Abstract: Supercapacitors (SCs) are a technology that assists in developing solutions to the rising energy demand that is a growing challenge today. The primary motivation for the latest technological research is the inevitable depletion of fossil resources. It is pertinent to mention critical challenges in this study, like how the generated energy would be conserved, its efficiency, and how to reduce environmental problems. As a result, SCs can be considered a major component of a diverse range of products (i.e., communication systems, military weapons systems, hybrid automobiles industry, uninterruptible power supplies, solar cells-based systems, and many more). SCs thrive due to their numerous technological benefits, including high power densities, fast charging / discharging cycles, and exceptionally long cycle life. This study briefly overviews SC classification before moving on to modeling and its practical applications. The state-of-the-art models for electrical, self-discharge and thermal behaviors are thoroughly evaluated for SC modeling based on electrochemical nature, equivalent electronic circuitry, intelligence, and fractional-order models for electrical behavioral simulation. The final section of this paper summarizes a wide variety of practical implementations of supercapacitors.