T-carbon is a novel carbon allotrope with many appealing properties. Since the proposal of T-carbon, there has been a lot of intensive studies devoted to its physical, chemical, optical, magnetic, thermoelectrical and topological properties and possible applications in diverse areas in recent years. In this review, we provide a comprehensive review on the advances of the experiments, intriguing properties and various potential applications of T-carbon in energy storage, optoelectronics, thermoelectrics, topological states, etc. As intercalation and doping are effective methods to modify the electronic structure of materials or even to convert into sparkly different new structures or phases, we also discuss different atom doped T-carbon, which exhibit more intriguing properties and lead to promising potential applications in solar cells, photocatalysis, magnetism, superconductivity and so on. In addition, it is interesting to mention that the hydrogenated T-carbon molecules were found to be possibly related to the physical origin of the UV extinction feature in interstellar medium that has been the half-century long unsolved puzzle. A number of novel derivative structures either derived or inspired from T-carbon are included as well. Finally, we give prospects and outlook for future directions of study on T-carbon and related structures.