The rapid development of neural networks has led to tremendous applications in image segmentation, speech recognition, and medical image diagnosis, etc. Among various hardware implementations of neural networks, silicon photonics is considered one of the most promising approaches due to its CMOS compatibility, accessible integration platforms, mature fabrication techniques, and abundant optical components. In addition, neuromorphic computing based on silicon photonics can provide massively parallel processing and high-speed operations with low power consumption, thus enabling further exploration of neural networks. Here, we focused on the development of neuromorphic computing based on silicon photonics, introducing this field from the perspective of electronic–photonic co-design and presenting the architecture and algorithm theory. Finally, we discussed the prospects and challenges of neuromorphic silicon photonics.