As a typical representative of nanomaterials, carbon nanomaterials have attracted widespread attention in the construction of electronic devices owing to their unique physical and chemical properties, multi-dimensionality, multi-hybridization methods, and excellent electronic properties. Especially in the recent years, memristors based on carbon nanomaterials have flourished in the field of building non-volatile memory devices and neuromorphic applications. In the current work, the preparation methods and structural characteristics of carbon nanomaterials of different dimensions were systematically reviewed. Afterwards, in depth discussion on the structural characteristics and working mechanism of memristors based on carbon nanomaterials of different dimensions was conducted. Finally, the potential applications of carbon-based memristors in logic operations, neural network construction, artificial vision systems, artificial tactile systems, and multimodal perception systems were also introduced. It is believed that this paper will provide guidance for the future development of high-quality information storage, high-performance neuromorphic applications, and high-sensitivity bionic sensing based on carbon-based memristors.