The paper provides a comprehensive survey on resource management in joint communication and computing-embedded space-air-ground integrated networks (JCC-SAGIN). It begins by reviewing the architecture, enabling technologies, and applications of JCC-SAGIN, emphasizing the integration of non-terrestrial platforms with processing capabilities. The paper then delves into resource management modeling and optimization methods, including traditional optimization techniques and learning-based intelligent decision-making frameworks. Finally, it outlines future research directions, highlighting the need for addressing the unique challenges of JCC-SAGIN, such as spatiotemporal dynamics, interdependence of large-scale resource variables, and trade-offs among performance metrics. The paper aims to fill gaps in the literature by providing a detailed review of the evolution of network integration and computing hardware in SAGIN, practical engineering applications, and theoretical resource management methods.The paper provides a comprehensive survey on resource management in joint communication and computing-embedded space-air-ground integrated networks (JCC-SAGIN). It begins by reviewing the architecture, enabling technologies, and applications of JCC-SAGIN, emphasizing the integration of non-terrestrial platforms with processing capabilities. The paper then delves into resource management modeling and optimization methods, including traditional optimization techniques and learning-based intelligent decision-making frameworks. Finally, it outlines future research directions, highlighting the need for addressing the unique challenges of JCC-SAGIN, such as spatiotemporal dynamics, interdependence of large-scale resource variables, and trade-offs among performance metrics. The paper aims to fill gaps in the literature by providing a detailed review of the evolution of network integration and computing hardware in SAGIN, practical engineering applications, and theoretical resource management methods.