Fault diagnostics and prognosis are vital functions of engineering systems, mainly fault prognosis, which is a relatively novel area and requires further development. By applying these methods, the system can be enriched with the ability to detect and isolate faults before they result in failures; in addition, fault propagation can be predicted, and maintenance can be considered to reduce the risk of severe failure. This paper focuses on the problem of satellite formation fault diagnosis and prognosis in the literature. Multi-satellite networks that cooperate as multi-agent systems are primarily used to implement cutting-edge technologies and improve future Earth and space observing missions. Space systems constantly encounter numerous failures due to the hazards and challenges of the space environment that need to be tackled. The current starts with an overview of the main concepts and motivations behind the deployment of small satellites in constellation settings and the detection and prediction of their faults. Next, recent papers on fault diagnosis and prognosis of single and multiple agent(s) or satellite(s), working individually or in collaboration, are reviewed. Comprehensive comparisons and categorization of the reviewed literature are included throughout the paper leading to existing research gaps for future work.