With increasing demand for low cost and high performance energy resources, rechargeable batteries, such as lithium ion batteries (LIBs) and sodium ion batteries (SIBs), have been intensively studied in recent years. The performance of existing anode materials for both LIBs and SIBs need substantial improvements in terms of energy capacity, rate capability, stability, safety and manufacturing cost to modernize the battery applications in electric vehicles (EV) and energy-saving smart electric grids. Graphene is considered an effective additive in fabricating composites for anode materials since it possesses high electrical conductivity, large surface area and excellent mechanical properties. Therefore, this thesis attempts to synthesize a series of graphene-based composites as anode materials for LIBs and SIBs, to address the aforementioned concerns. To date, numerous methods have been developed for the fabrication of graphene composites; however, most of them are sophisticated, complex, not scalable and therefore expensive. A wet-mechanochemical (wet ball-milling) method that is simple, rapid, facile, economic and most importantly, can be up-scaled for mass production is proposed to address these issues.