Abstract: Satellites have been widely regarded as an important part in 6G networks. Satellite computing networks can comprehensively involve real-time networking and computing resources, schedule different applications to appropriate computing nodes, meet the latency requirements of diverse services, and finally facilitate the efficient utilization of on-orbit communication, processing, storage and other resources. First, the concept of satellite computing networks is exhibited, along with the status and trend of satellite communication networks. Then, satellite computing networks are designed from three aspects, overall architecture, hardware structure, and software architecture. Finally, the technical challenges faced by satellite computing networks are summarized with the future work.