With the need of the inteet of things, big data, and artificial intelligence, creating new computing architecture is greatly desired for handling data-intensive tasks. Human brain can simultaneously process and store information, which would reduce the power consumption while improve the efficiency of computing. Therefore, the development of brain-like intelligent device and the construction of brain-like computation are important breakthroughs in the field of artificial intelligence. Memristor, as the fourth fundamental circuit element, is an ideal synaptic simulator due to its integration of storage and processing characteristics, and very similar activities and the working mechanism to synapses among neurons which are the most numerous components of the brains. In particular, memristive synaptic devices with optoelectronic responding capability have the benefits of storing and processing transmitted optical signals with wide bandwidth, ultrafast data operation speed, low power consumption, and low cross-talk, which is important for building efficient brain-like com-puting networks. Herein, we review recent progresses in optoelectronic memristor for neuromorphic computing, including the optoelectronic memristive materials, working principles, applications, as well as the current challenges and the future development of the optoelectronic memristor.