This article reviews new superconducting phases of carbon-based materials. During the past decade, new carbon-based superconductors have been extensively developed through the use of intercalation chemistry, electrostatic carrier doping, and surface-proving techniques. The superconducting transition temperature T-c of these materials has been rapidly elevated, and the variety of superconductors has been increased. This review fully introduces graphite, graphene, and hydrocarbon superconductors and future perspectives of high-T-c superconductors based on these materials, including present problems. Carbon-based superconductors show various types of interesting behavior, such as a positive pressure dependence of T-c. At present, experimental information on superconductors is still insufficient, and theoretical treatment is also incomplete. In particular, experimental results are still lacking for graphene and hydrocarbon superconductors. Therefore, it is very important to review experimental results in detail and introduce theoretical approaches, for the sake of advances in condensed matter physics. Furthermore, the recent experimental results on hydrocarbon superconductors obtained by our group are also included in this article. Consequently, this review article may provide a hint to designing new carbon-based superconductors exhibiting higher T-c and interesting physical features.