A flexible, asymmetric electrochemical cell comprising: (A) A sheet of graphene paper as first electrode comprising nano graphene platelets having a platelet thickness less than 1 nm, wherein the first electrode has electrolyte-accessible pores; (B) A thin-film or paper-like first separator and electrolyte; and (C) A thin-film or paper-like second electrode which is different in composition than the first electrode; wherein the separator is sandwiched between the first and second electrode to form a flexible laminate configuration. The asymmetric supercapacitor cells with different NGP-based electrodes exhibit an exceptionally high capacitance, specific energy, and stable and long cycle life.