This review article provides an exhaustive survey on experimental investigations regarding the thermal stability assessment of polymers and polymer-based composites intended for applications in the aeronautical and space fields. This review aims to: (1) come up with a systematic and critical overview of the state-of-the-art knowledge and research on the thermal stability of various polymers and composites, such as polyimides, epoxy composites, and carbon-filled composites; (2) identify the key factors, mechanisms, methods, and challenges that affect the thermal stability of polymers and composites, such as the temperature, radiation, oxygen, and degradation; (3) highlight the current and potential applications, benefits, limitations, and opportunities of polymers and composites with high thermal stability, such as thermal control, structural reinforcement, protection, and energy conversion; (4) give a glimpse of future research directions by providing indications for improving the thermal stability of polymers and composites, such as novel materials, hybrid composites, smart materials, and advanced processing methods. In this context, thermal analysis plays a crucial role in the development of polyimide-based materials for the radiation shielding of space solar cells or spacecraft components. The main strategies that have been explored to improve the processability, optical transparency, and radiation resistance of polyimide-based materials without compromising their thermal stability are highlighted. The combination of different types of polyimides, such as linear and hyperbranched, as well as the incorporation of bulky pendant groups, are reported as routes for improving the mechanical behavior and optical transparency while retaining the thermal stability and radiation shielding properties. Furthermore, the thermal stability of polymer/carbon nanocomposites is discussed with particular reference to the role of the filler in radiation monitoring systems and electromagnetic interference shielding in the space environment. Finally, the thermal stability of epoxy-based composites and how it is influenced by the type and content of epoxy resin, curing agent, degree of cross-linking, and the addition of fillers or modifiers are critically reviewed. Some studies have reported that incorporating mesoporous silica micro-filler or microencapsulated phase change materials (MPCM) into epoxy resin can enhance its thermal stability and mechanical properties. The mesoporous silica composite exhibited the highest glass transition temperature and activation energy for thermal degradation among all the epoxy-silica nano/micro-composites. Indeed, an average activation energy value of 148.86 kJ/mol was recorded for the thermal degradation of unfilled epoxy resin. The maximum activation energy range was instead recorded for composites loaded with mesoporous microsilica. The EMC-5p50 sample showed the highest mean value of 217.6 kJ/mol. This remarkable enhancement was ascribed to the polymer invading the silica pores and forging formidable interfacial bonds.