As one of the most versatile elements, carbon materials occupy the most plentiful allotropies composed of pure or mixed hybridization orbitals of sp1/sp2/sp3. The design and synthesis of new carbon materials may be stimulated based on a deeper understanding of underlying structures and related properties. In this review, the initial early discoveries of carbon materials are examined based on their hybridization of orbitals. According to the type of hybridization, the discovered carbon materials are firstly classified and introduced in detail based on their crystal structures. Secondly, its physical and chemical properties, mainly including mechanical properties, optical properties and electronic properties, are reviewed. Thirdly, the existing methods of predicting carbon structure and synthesizing carbon materials are classified and summarized, and some typical carbon materials predicted or prepared are discussed respectively. Then, the main applications of newly synthesized carbon materials in the last two decades are classified and summarized, and the microstructure is linked with the macro properties and specific applications. Finally, the future research opportunities for carbon materials and their potential applications are prospected from the aspects of the gap between theoretical prediction and preparation, the current research hotspot of carbon materials and the incomplete application of carbon materials. It is the authors' intention for this review paper to serve not only as a valuable reference for research into carbon materials and related composites, but also as a guidance for novel materials design at the atomic level.