Abstract: With the continuous evolution of the 6th generation mobile communication system (6G), the space–air–ground integrated network (SAGIN) has emerged as a key component for achieving seamless interconnection among satellites, aerial platforms, and terrestrial networks. By integrating satellite constellations, aerial platforms, and terrestrial communication infrastructures, SAGIN aims to support high-throughput, ultra-reliable, and low-latency communication services on a global scale. It plays a critical role in enabling emerging applications such as emergency communication, intelligent transportation, environmental monitoring, remote sensing, and military surveillance. However, SAGIN’s highly dynamic topology, heterogeneous network structure, broad resource distribution, and uneven link quality introduce considerable challenges for efficient network management, resource allocation, and system optimization. Conventional rule-based and model-driven methods, constrained by limited adaptability and computational efficiency, can hardly meet the requirements of the large-scale, time-varying, and cross-domain intelligent networks envisioned in 6G. In this context, artificial intelligence (AI) has become a transformative enabler of SAGIN’s intelligent evolution, offering powerful capabilities in perception, representation learning, reasoning, and autonomous decision-making. The integration of AI equips SAGIN with the ability to sense the communication environment, learn from data-driven experiences, and dynamically adapt network strategies in real time. This study provides a comprehensive analysis of AI-enabled optimization mechanisms for SAGIN, focusing on their roles in achieving self-organization, predictive control, and collaborative decision-making. It first examines the overall architecture and key features of SAGIN, emphasizing its hierarchical, multi-layer composition and cross-domain interconnectivity across space, air, and ground. It then reviews major AI paradigms and their suitability for network optimization, including machine learning (ML), graph neural networks (GNN), and reinforcement learning (RL). ML enables data-driven modeling and knowledge extraction, GNNs effectively capture spatial–temporal dependencies among dynamically changing network nodes, and RL supports adaptive decision-making and self-optimization in uncertain communication environments. Building on these foundations, the study explores typical AI-driven applications in SAGIN, such as intelligent resource management, mobility management and routing optimization, aerial platform trajectory planning, and task offloading with collaborative computation. Through these intelligent mechanisms, AI facilitates efficient resource orchestration, predictive control, and autonomous optimization across heterogeneous domains, thereby enhancing network performance, reliability, and scalability. AI-based cooperative decision frameworks further enable multi-agent coordination among satellites, unmanned aerial vehicles, and ground nodes, supporting distributed intelligence and dynamic network adaptation in real time. Finally, the study identifies several critical challenges and open research directions in integrating AI with SAGIN. These challenges include achieving efficient model deployment under resource constraints, ensuring robust learning in highly dynamic environments, maintaining data security and privacy, and establishing trustworthy and explainable AI mechanisms. Future research is expected to focus on federated and distributed intelligence, intent-driven autonomous network control, and the deep convergence of large AI models with cross-layer and cross-domain optimization frameworks. Moreover, the evolution toward cognitive and semantic communication will enable SAGIN to shift from data transmission to knowledge interaction, supporting a new paradigm of intelligent connectivity. Overall, this study provides a comprehensive overview of AI’s role in SAGIN optimization and offers insights for building an intelligent, resilient, and globally integrated 6G communication ecosystem that bridges the physical and digital worlds.