Driven by the rapid advancement of the Internet of Things and artificial intelligence, computational power demands have experienced an exponential surge, thereby accentuating the inherent limitations of the conventional von Neumann architecture. Neuromorphic computing memristors are emerging as a promising solution to overcome this bottleneck. Among various material-based memristors, carbon-based memristors (CBMs) are particularly attractive due to their biocompatibility, flexibility, and stability, which make them well suited for next-generation neuromorphic applications. This review summarizes the recent advancements in CBMs and proposes potential application scenarios in neuromorphic computing. Representative CBMs and preparation methods of carbon-based materials in different dimensions (0D, 1D, 2D, and 3D) are presented, followed by structural, storage, and synaptic plasticity testing and switching mechanisms. The neural network architecture built by CBMs is summarized for image processing, wearable electronics, and three-dimensional integration. Finally, the future challenges and application prospects of CBMs are reviewed and summarized.