Space anomaly detection is of paramount importance in ensuring the safety and reliability of space systems, particularly in the face of increasing threats. This comprehensive survey article focuses on the unique challenges encountered in space security and provides a thorough analysis and synthesis of state-of-the-art anomaly detection systems. The survey identifies key challenges such as scalability, real-time detection, limited labeled data, concept drift, and adversarial attacks, setting the stage for future research in the field. By extensively reviewing existing approaches and methods, the article evaluates their strengths, limitations, and potential applications in space networks. It goes beyond a mere summary by introducing an innovative integration of stream-based and graph-based methods for dynamic space anomaly detection. This integration not only opens up new avenues for research but also enhances detection accuracy by capturing the complex temporal and structural dependencies within space networks. By pioneering research in space security, this survey article offers valuable insights, lessons, and guidance for researchers, engineers, and practitioners in the field of space anomaly detection. It acknowledges the increasing number and sophistication of space threats and addresses the urgent need for innovative approaches to detect anomalies within space networks. With the knowledge and recommendations provided, the space industry can enhance its anomaly detection capabilities, mitigate risks, and safeguard the integrity and security of space systems.