The critical energy crisis and environmental pollution associated with the fast fossil fuels consumption has greatly motivated the research and development of clean energy. Up to date, increasing attention has been put into renewable energy sources such as wind, solar, tidal, biomass, and geothermal. However, these energy sources are intermittent and not stable in nature, which bring an advanced energy storage system on request. The electrochemical energy storage (EES) system is considered very promising for effective and efficient usage of clean energy and therefore has been intensively investigated during past decades.Lithium ion batteries (LIBs) are the most ubiquitous energy storage system among EES, which is commonly used in portable electronic devices and electric vehicles, due to their long cycle life, high energy density, and high stability. However, most cathodes (e.g. lithium-insertion compounds) and anodes (e.g. graphite and silicon) suffer from either low intrinsic electrical conductivity or poor lithium diffusivity, limiting the power density of LIBs. To date, constructing a matrix with high electrical conductivity and Li+ diffusion rate to form composite electrodes is one of the most effective ways to address the current challenges. Carbon materials with excellent intrinsic conductivity and good designability are a good candidate to be applied in the composite electrode. Particularly, graphene is proposed as a conductive agent or act as a carbon matrix to form a composite electrode with other active electrode materials due to its excellent electron conductivity (2000 S cm-1)1, high surface area (2630 m2 g-1) 2 and high ambipolar charge-carrier mobility (105 cm2 V-1 s-1)3. Such graphene composite electrodes are generally synthesized through a direct assembly or bottom-up growth, of which the former approach disperses graphene (or perhaps graphene oxide) with a precursor or an active material itself followed by a hydrothermal or spray-dry methods respectively to assemble the composites, while the later approach converts carbon precursor to graphene on the surface of active materials through chemical vapour deposition (CVD). The direct assembly approach needs graphene with high dispersity which is associated with the degree of functionalization. However, such functionalized groups lead to defects and low conductivity. Despite the extensive efforts made, making graphene with both high conductivity and dispersibility remains challenging. The bottom-up growth approach usually applied the “substrate-graphene” after CVD to produce composite material or directly use it as an active material for LIBs. However, such precursors or active materials mostly have inappropriate catalytic property or cannot catalyze the formation of high-quality graphene at all, which gives a strict restriction on choosing substrates.In this dissertation, we design and synthesize edge-functionalized graphene with large lateral size (10 �m) to address the paradox of the direct assembly approach, such that the functional groups in the edge can provide the graphene with high dispersibility (10 mg mL-1 in water), while the well-retained graphene structure in the basal plane can provide the graphene with high conductivity (924 S cm-1). The edge-functionalized graphene can be readily synthesized using an edge-to-interior exfoliation strategy based on a controllable catalytic reaction between H2O2 and FeCl3-graphite intercalation compound, which improves processing capability in composite fabrication and enables excellent conductivity as a conductive network in batteries.Such edge-oxidized graphene (eoG) was then complexed with commercial LiFePO4 as an example of its broad applications through a spray drying method. During the synthetical process, the large-size eoG anchored with commercial LFP nanoparticles folds, twists and encapsulates into spherical LFP-eoG composite, which minimize the lithium ion diffusion length, as well as the contact resistance between stacked graphene network and LFP, enabling effective transport of Li+ and electrons. Such LFP-eoG composite cathode exhibits high reversible capacity (159.9 mA h g-1 at 0.5 C) and excellent rate performance (76.6 mAh g-1 at 20 C), which is 12 folds higher than LFP-GO with the same carbon content and 16 folds higher than commercial LFP (our primary particles of LFP-eoG). Moreover, the dense spherical morphology contributes to a higher tap density (1.2 g cm-3), enabling high volumetric capacity of LFP-eoG composite electrodes (e.g. 193.8 mA h mL-1 at 0.5 C and 91 mA h mL-1 at 20 C).Inspired by the graphite intercalation compounds (GICs) route to obtain eoG, we fabricate carbon nanotubes (CNTs) embedded graphite anode for high-power LIBs. Such CNT-graphite anode was synthesized through an intercalation of catalyst into graphite interlayers and the following CVD growth of CNTs. These embedded CNTs expand the interlayer spacing of graphite and act as a transit reservoir for Li+, which improve the lithium ion diffusion rate as well as electrical conductivity, enabling high reversible capacity (291.9 mA h g-1 at 1 C) and good rate performance (61.1 mAh g-1 at 5 C) for lithium ion batteries.