Carbon-based materials strongly pertain to citizens’ daily life due to their versatile derivatives such as diamond, graphite, fullerenes, carbon nanotube, single-layer graphene, and amorphous carbon (a-C). Compared to other families, a-C exhibits reconfigurable electrical properties by triggering its sp2–sp3 transition and vice versa, which can be readily fabricated by conventional film deposition technologies. For above reasons, a-C has been adopted as a promising memristive material and has given birth to several physical and theoretical prototypes. To further help researchers comprehend the physics behind a-C-based memristors and push forward their development, here we first reviewed the classification of a-C-based materials associated with their respective electrical and thermal properties. Subsequently, several a-C -based memristors with different architectures were presented, followed by their respective memristive principles. We also elucidated the state-of-the-art modeling strategies of a-C memristors, and their practical applications on neuromorphic fields were also described. The possible scenarios to further mitigate the physical performances of a-C memristors were eventually discussed, and their future prospect to rival with other memristors was also envisioned.