The development of an electromagnetic spectrum monitoring (ESM) system based on a low-earth orbit (LEO) constellation has shown to be an effective method of achieving global ESM and is now a research hotspot in several fields. In the classic LEO-based ESM system, the “on-satellite acquisition and processing” architecture is used in which the satellite gathers and analyzes electromagnetic signal data before transmitting the processed results back to the data center on the ground. Although this framework can reduce the transmission pressure on the satellite-ground link, it yields a limited system performance of the single satellite payload. This paper proposes an intelligent processing framework for the LEO-based ESM system with separate acquisition and processing. In this framework, the satellites serve as forwarding nodes for electromagnetic signal data. The satellites are only responsible for acquiring electromagnetic signal data, which is then processed by a data center on the ground. Unlike the traditional framework, this framework delivers massive amounts of raw electromagnetic data to the ground. To address the problem that the massive data in this framework are difficult to process using traditional technical methods, deep learning is organically integrated with the key technologies of the traditional framework. Deep learning provides a new option for realizing global space–time continuous ESM. The three key technologies involved in the proposed framework are spectrum sensing, blind source separation, and passive positioning based on deep learning, and their research progress in recent years has been sorted out. Compared with ground-based systems, constellation-based systems have the following characteristics: (1) the satellites are far away from the radiation source; (2) the satellites are fast; (3) the satellites show long-distance distribution among them; (4) the topology of the constellation is always in high-speed dynamic change. These characteristics cause a significant divergence between their essential technologies and the research of ground-based systems for these technologies. However, the present efforts relating to essential technologies are based on research conducted on ground-based platforms. There is an issue of applicability to consider when immediately transitioning them to the constellation-based system. Thus, the suitability of each important technology for the migration of constellation-based systems is thoroughly examined. The future trajectory of each major technological breakthrough is then investigated. Finally, recommendations for further studies are made based on the leading technologies of the intelligent processing framework for LEO-based ESM systems.