Graphene, the one-atom-thick sheet of sp2-hybridized carbon atoms, ever since its advent in the scientific world, has enjoyed a star status. Owing to its unique structure, graphene is known to have extraordinary physical and chemical properties, such as very high electrical conductivity, exceptionally high surface area, and phenomenal mechanical strength. All these properties make graphene particularly attractive for its application in electrochemical capacitors (ECs), also known as supercapacitors. This chapter focuses on the fundamentals of a capacitor, different types of electrochemical capacitors, including electrochemical double-layer capacitors, pseudocapacitors, asymmetric or "hybrid" capacitors; and the applicability of graphene to each of these supercapacitor classes. One section of this chapter is dedicated to the emerging field of microsupercapacitors and the application of graphene as a material for microsupercapacitors. The chapter concludes with a summary and an outlook for further improvements to the currently existing works.