Renewable and non-renewable energy harvesting and its storage are important components of our everyday economic processes. Lithium-ion batteries (LIBs), with their rechargeable features, high open-circuit voltage, and potential large energy capacities, are one of the ideal alternatives for addressing that endeavor. Despite their widespread use, improving LIBs’ performance, such as increasing energy density demand, stability, and safety, remains a significant problem. The anode is an important component in LIBs and determines battery performance. To achieve high-performance batteries, anode subsystems must have a high capacity for ion intercalation/adsorption, high efficiency during charging and discharging operations, minimal reactivity to the electrolyte, excellent cyclability, and non-toxic operation. Group IV elements (Si, Ge, and Sn), transition-metal oxides, nitrides, sulfides, and transition-metal carbonates have all been tested as LIB anode materials. However, these materials have low rate capability due to weak conductivity, dismal cyclability, and fast capacity fading owing to large volume expansion and severe electrode collapse during the cycle operations. Contrarily, carbon nanostructures (1D, 2D, and 3D) have the potential to be employed as anode materials for LIBs due to their large buffer space and Li-ion conductivity. However, their capacity is limited. Blending these two material types to create a conductive and flexible carbon supporting nanocomposite framework as an anode material for LIBs is regarded as one of the most beneficial techniques for improving stability, conductivity, and capacity. This review begins with a quick overview of LIB operations and performance measurement indexes. It then examines the recently reported synthesis methods of carbon-based nanostructured materials and the effects of their properties on high-performance anode materials for LIBs. These include composites made of 1D, 2D, and 3D nanocarbon structures and much higher Li storage-capacity nanostructured compounds (metals, transitional metal oxides, transition-metal sulfides, and other inorganic materials). The strategies employed to improve anode performance by leveraging the intrinsic features of individual constituents and their structural designs are examined. The review concludes with a summary and an outlook for future advancements in this research field.