Few-layer exfoliated graphene platelets are ultrathin particles of graphite that can also be thought of as short stacks of graphene sheets prepared through proprietary manufacturing processes. Several grades and sizes with thicknesses ranging from 1-20 nanometers and width ranging from 1-50µm are manufactured by XG Sciences, Lansing, MI, USA. Unique manufacturing processes for these platelet materials are non-oxidizing; thus, yielding a pristine graphitic surface of sp2 carbon molecules. This makes these platelet particles especially suitable for applications requiring high electrical and thermal conductivities. The surface areas of the resulting platelets predominantly consist of the open surface areas of the graphene basal planes. Open surface areas of the graphene basal planes as well the interlayer spaces between the graphene sheets coupled with high electrical conductivities are an important criteria for electrodes in many electrochemical energy storage technologies. Unique morphology of the platelets offer the potential to structure self-standing electrodes by doing away with inactive components such as current collectors and thus, enhance the energy density. Surface modification of the platelets through the deposition of transition metal oxides on the graphene basal planes has the potential to enhance the energy storage capacity due to the participation of two different components in the energy storage process. Few-layer exfoliated graphene platelets can be dispersed in various aqueous and non-aqueous solvents depending upon the nature of the interaction between their surfaces and the solvent molecules. Sometimes this nature of interaction can be altered by modifying the surfaces of the few-layer exfoliated graphene platelets with polymer surfactants that can control their hydrophobicity or hydrophilicity. Transition metal oxides can be deposited on few-layer exfoliated graphene platelet surface through the interaction with precursor materials in wet-chemical synthesis procedure. Presence of polymer surfactants in the synthesis procedure can bring in even further surface interaction phenomena and alter the structure of the deposited transition metal oxides. Dispersions of few-layer exfoliated graphene platelets and composites with transition metal oxides can be used to manufacture electrode structures either by coating directly onto metallic substrates with the help of a binder material or through the fabrication of self-standing structures without a binder material. Two types of few-layer exfoliated graphene platelets have been investigated in this research: Grade-M particles (15µm average diameter) have an average thickness of approximately 6-8 nanometers and a typical surface area of 120-150 m²/g; and Grade-C, generally consisting of aggregates of particles with diameter less than 2µm and a particle thickness of few nanometers with a surface area of 750 m²/g. First part of this research investigated platelets with different surface areas, particle sizes and structures combined with an aqueous electrolyte as electric double-layer capacitor electrode materials. A binder free self-standing bilayer composite electrode fabricated with Grade-M particles and Grade-C particles was found to retain near-ideal double-layer capacitive characteristics at high scan rate. Reasonably high specific capacitance values normalized with respect to both the weight of the Grade-C particles and the weight of the self-standing electrode were obtained at high current rate. Small equivalent series resistance (ESR) and charge transfer resistance (R_ct) of the self-standing electrode was found to be the cause of this desirable behavior. Second part of this research investigated a  composite of Birnessite-MnO₂ with Grade-M platelet as a redox capacitor electrode material in a self-standing structure. It was found that a self-standing electrode with Birnessite-MnO₂ coated platelet exhibits improved impedance characteristics compared to pure Grade-M platelet based electrode. This may be explained by the fact that the platelets remain separated in the electrode structure due to the metallic deposition and thus, improving the impedance characteristics.