The ultrathin two-dimensional structure and unique properties of graphene make it highly attractive for high-performance asymmetric supercapacitors (ASCs), which are generally constructed by two different materials as positive electrode and negative electrode, respectively, in an asymmetric configuration. Here, a deep insight into the recent advances of graphene-based materials for high-voltage and high-energy asymmetric supercapacitors (ASCs) is presented. First, the critical aspects that directly affect the performance of ASCs and how they have been tackled in terms of the assembly principle of ASCs and standard methods of accurate performance evaluation are discussed. Second, the major categories and the state-of-the-art positive and negative electrode materials of ASCs are described. Third, the latest advances of different graphene-based nano-architectures, such as reduced graphene oxide, porous graphene, graphene quantum dots, graphene nanoribbons, graphene fibers, graphene films, graphene aerogels, graphene foams, and various hybrids of graphene-carbon nanotubes, graphene-metal oxides and graphene-conducting polymers, for ASCs are summarized. Fourth, major performance parameters, including high voltage, high capacitance, high power and high energy devices, as well as new device geometry of planar and all-solid-state devices, are described in details, highlighting the uniqueness and superiority of graphene for hybrid energy storage. Fifth, The elaborated screening of graphene-based materials with controllable morphologies, two-dimensional and three-dimensional well-defined nanostructures, and tailored compositions, architectures of the electrode, selection of electrolytes, and optimized integrity of different device components are overviewed. Finally, future perspectives and challenges of graphene-based ASCs are discussed.