This paper explores how to optimize the operation of large satellite networks using artificial intelligence (AI), based on the European Space Agency (ESA) ConstellAI project. The consortium consisting of GMV GmbH, Saarland University, and Thales Alenia Space developed an AI-based algorithm that proved more efficient than existing methods for two major operational tasks: data routing and resource allocation. Reinforcement learning (RL) was used to improve the end-to-end latency of data routing, and task scheduling was optimized for resource allocation to efficiently use limited resources such as batteries and memory. Experiments on various satellite configurations and operational scenarios demonstrate that RL offers superior flexibility, scalability, and generalization performance compared to existing methods, and is essential for autonomous and intelligent satellite management. The results suggest that AI can provide a more adaptive, robust, and cost-effective satellite network management solution.