With the developed tools for nanoscale analysis, the synthesis and understanding of nanostructured carbon materials have further expanded their fields and applications. Various synthesis methods have been investigated with the aid of advanced nanostructural analysis for nanostructured carbon materials, including arc discharge, template carbonization, conversion of graphene oxides to their reduced analog, fine organic synthesis, topochemical pyrolysis, and chemical vapor deposition (CVD). Consequently, many advanced carbon materials, including carbon fibers, carbon nanotubes (CNTs), graphenes, structural graphite, and carbon foams have been developed with improved physicochemical properties, and they are growing at a compound average growth rate (CAGR) of ~6% with an annual global market of 3 billion USD in 2015. They are extensively used as adsorbents, catalysts, and catalyst supports, conductive additives, and anode materials in batteries, supercapacitors, polymer-electrolyte fuel cells (PEFCs), and photothermal conversion. In this context, the chemical science of two-dimensional (2D) graphene and its zero-dimensional (0D) and one-dimensional (1D) analogs have been extensively studied in recent decades. Graphene, a 2D-carbon material, was originally prepared by exfoliation, and its synthesis, analysis, and applications have been extensively investigated. Single-plate graphene materials have high electrical conductivity and high thermal/chemical stability; therefore, they are suitable for practical applications in energy-related devices. A class of 1D-graphene, carbon nanotubes and cylindrical analogs, has also been investigated for electrochemical and catalysis applications owing to their high electrical conductivity. A challenging aspect is the synthesis of the corresponding 3D graphene materials from a 2D scaffold. Reducing the dimension of 2D graphene can be used to develop 3D graphene; the 0D analog of the fullerene family, a good electron acceptor, can be used as a building block to develop 3D-analogs. Catalytic carbonization has also been successfully applied to prepare 3D graphene architecture. However, the precise synthesis of 3D-ordered graphene materials with well-defined negatively-curved 3D networks remains an emerging topic since British scientists predicted imaginary carbon frameworks with 8membered rings in hexagons to achieve a 3D structure with low strain. These materials are highly symmetric and possess highly ordered nanostructures that provide various fascinating functions (vide infra). For example, material surfaces for the adsorption of gases should be as homogeneous as possible with respect to the structure and chemical composition for better and faster reactions, and imaginary 3D-ordered carbon frameworks should meet these criteria. The novel electronic nature of these frameworks makes them appealing for various applications.