Superconductors would exhibit unique quantum properties below the critical transition temperatures, including zero-resistance and complete diamagnetism (the Meissner effect) and have potential revolutionary application in fields of energy transmission and transportation. Therefore, the exploration of high-temperature superconductors with transition temperature exceeding the liquid nitrogen boiling point (77 K) has remained a central issue in condensed matter physics. Based on the Bardeen-Cooper-Schrieffer (BCS) theoretical framework, more studies reveal that the light-element compounds with strong covalent bonds (like boron-carbon-based systems) can also exhibit strong electron-phonon coupling, which is similar to the hydrogen rich superconductors. Moreover, it can show high superconducting transition temperatures and can display excellent structural stability under sub-megabar pressures. For example, the MgB₂ and its derivatives, such as layered boron-carbon superconductors, sodalite-like cage-structured boron-carbon systems, and other boron-carbon-based superconductors, have received more attention in the field of boron-carbon-based superconductors. In this paper, we reviewed the recent progresses in boron-carbon-based superconductors, systematically analyzed the mechanism of its superconductivity, and discuss future challenges in discovering more high-temperature superconductors within this material family.