In pursuit of solving the foreseeable depletion of fossil energies and environmental pollution caused by combustion of them, great efforts have been devoted to exploring renewable and clean energies, like the solar energy, nuclear energy, and geothermal energy, etc. as well as the technologies in converting these new energies into the form of usable electricity. In this regard, (rechargeable) zinc-air batteries and fuel cells have demonstrated promising potentials due to their large output energy density, power density and more importantly, their environmental compatibility. To consume oxygen molecules at cathode, these devices suffer greatly from the large overpotential and sluggish kinetics from the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). Platinum, iridium and other noble metal-based electrocatalysts (NMCs) are conventionally used at the cathode of zinc-air batteries and fuel cells. However, the NMCs are subjected to high cost and insufficient durability. Thus, substituting the NMCs with other earth-abundant elements is currently imperative for the large-scale commercialization of the zinc-air batteries and fuel cells. Within this framework, this thesis attempts to utilize graphene as the building blocks to couple with other active elements, e.g. transition metal ions and nitrogen doped disordered carbon to fabricate advanced electrocatalysts for OER and ORR. A series of synthesizing methods have been developed to synthesize the graphene-based nanocomposites, including room-temperature coordination adsorption, hydrothermal treatment, and high-temperature calcination, etc. The physical features of the resultant nanocomposites have been thoroughly investigated by using XRD, SEM, and TEM. Meanwhile, their electrochemical performances were explored in terms of the potential-current response and the corresponding working durability. Besides, the associated origin of their intrinsic activity has been investigated and discussed. Molecular Ni–/Co–porphyrin multilayers were spontaneously adsorbed on the surface of graphene sheets layer-by-layer via non-covalent forces such as Van der Waals’ force and π-π interactions. It was observed that the electrochemical performance of the nanocomposite could be tuned by controlling the number of the Ni–/Co–porphyrin layers on the surface of graphene. This is ascribed to the counterbalance between the steric hindrance and the content of the active species. Such research work manifested the controllability of the OER/ORR performance at the molecular level and revealed the essential influence between the content of the active sites and the steric hindrance caused by their spatial accommodation. To implement a low-cost and scalable synthesis strategy, carbon black NPs and amorphous CoBi nanoplates were assembled with graphene to build a sandwich-like nanocomposite by use of amphipathicity of graphene oxide. The obtained sandwich-like nanocomposite exhibited excellent ORR/OER performance, which was comparable to the state-of-the-art materials. The performance enhancement towards ORR was assigned to the enlarged accessible active surface area of the nanocomposite catalyst. Without changing the chemical composition of the active species, this work highlighted the significance of the rational design of the geometrical configuration by means of the non-covalent force in an electrocatalyst. The resultant nanocomposite was further assembled in a rechargeable zinc-air battery to demonstrate its practicability. The lack of the high-efficiency and noble metal-free electrocatalyst in the acid media has been an intractable problem for years. To address this issue, a disordered carbon layer impregnated with Co-N on the surface of graphene sheet was fabricated by pyrolysing the hydrothermal product of graphene oxide and cobalt gluconate. The resultant nanocomposite exhibited remarkable activity to ORR in both alkaline and acid media, which was due to the high dispersion of abundant active sites. Moreover, different active working sites in alkaline and acid condition for the obtained material were suggested. This inspired us to investigate different roles of the metal species in the ORR electrocatalysts. For the nitrogen-doped carbon materials, the pyridinic nitrogen doping is believed to possess the highest activity for ORR in alkaline environment. To verify that theory and further enhance the activity of the nitrogen-doped carbon materials, an ultrathin holey carbon layer coupled with graphene nanosheets was prepared. The edge enriched feature makes it easier to form pyridinic nitrogen during the nitrogen doping process. The obtained composite displayed the expected outstanding ORR performance in alkaline media and even surprisingly high activity in acid solution. The rationality of the design of this material was manifested by solving the commonly encountered insufficient charge transfer ability and stability of the holey graphene materials while preserving the high activity in the holey carbon sites. In a nutshell, this thesis contributes to the exploration of the graphene-based OER/ORR electrocatalyst in the aspects of i) tuning the electrochemical activity of the transition metal based electrocatalyst at the molecular level; ii) isolating and highlighting the significance in geometrical configuration of the ORR electrocatalyst with respect to kinetic process; iii) suggesting and verifying the different active sites of the same electrocatalyst tested under different pH values; iv) selectively inducing the formation of the active pyridinic nitrogen species in the ultrathin holey carbon layer coupled on the surface of graphene nanosheet.