Supercapacitors, with ultrahigh power density, superior rate capability, long-term cyclability, and exceptional safety, are regarded as one highly competitive candidate of electrochemical energy storage devices, filling the gap between batteries and conventional capacitors. Despite of tremendous effort, elaborated screening of high-performance electrode materials, e.g., graphene, is still intensively required. In this review, we describe the most recent progress in the research and development of graphene-based materials for high-performance and new-concept supercapacitors for the targeted applications in next-generation and smart electronics. First, the design and fabrication of high-performance supercapacitors, including electrical double layer capacitors, pseudocapacitors and hybrid supercapacitors, were summarized in term of the charge storage mechanism. Second, new-concept supercapacitors with multiple functionalities of high-voltage, fiber-shape, microscale and shape-diversity in order to fulfill the requirements of future electronics are reviewed. Accordingly, special emphasis is given to the structure-dependent-performance effects of pores, hybridization, dimensionalities of graphene-based materials on performance of supercapacitors, and tremendous potential of graphene-based planar micro-supercapacitors for the direct seamlessly integration with versatile micro-electronics. Finally, perspectives and challenges of graphene-based supercapacitors are briefly discussed.