Conventional computers based on the von Neumann architecture are inefficient in parallel computing and self-adaptive learning, and therefore cannot meet the rapid development of information technology that needs efficient and high-speed computing. Owing to the unique advantages such as high parallelism and ultralow power consumption, bioinspired neuromorphic computing can have the capability of breaking through the bottlenecks of conventional computers and is now considered as an ideal option to realize the next-generation artificial intelligence. As the hardware carriers that allow the implementing of neuromorphic computing, neuromorphic devices are very critical in building neuromorphic chips. Meanwhile, the development of human visual systems and optogenetics also provides a new insight into how to study neuromorphic devices. The emerging optoelectronic neuromorphic devices feature the unique advantages of photonics and electronics, showing great potential in the neuromorphic computing field and attracting more and more attention of the scientists. In view of these, the main purpose of this review is to disclose the recent research advances in optoelectronic neuromorphic devices and the prospects of their practical applications. We first review the artificial optoelectronic synapses and neurons, including device structural features, working mechanisms, and neuromorphic simulation functions. Then, we introduce the applications of optoelectronic neuromorphic devices particularly suitable for the fields including artificial vision systems, artificial perception systems, and neuromorphic computing. Finally, we summarize the challenges to the optoelectronic neuromorphic devices, which we are facing now, and present some perspectives about their development directions in the future.