Neural electrodes are used for acquiring neuron signals in brain-machine interfaces, and they are crucial for next-generation neuron engineering and related medical applications. Thus, developing flexible, stable and high-resolution neural electrodes will play an important role in stimulation, acquisition, recording and analysis of signals. Compared with traditional metallic electrodes, electrodes based on graphene and other two-dimensional materials have attracted wide attention in electrophysiological recording and stimulation due to their excellent physical properties such as unique flexibility, low resistance, and high optical transparency. In this review, we have reviewed the recent progress of electrodes based on graphene, graphene/polymer compounds and graphene-related materials for neuron signal recording, stimulation, and related optical signal coupling technology, which provides an outlook on the role of electrodes in the nanotechnology-neuron interface as well as medical diagnosis.