With the widespread application of Global Navigation Satellite Systems (GNSS) in critical industries such as transportation, aviation, maritime, communications, and finance, the increasing incidence of GNSS interference has become a global threat to the security of Positioning, Navigation, and Timing (PNT) services. Constrained by limited coverage and deployment density, traditional ground-based interference monitoring systems cannot provide continuous global-scale monitoring capability. Low Earth Orbit (LEO) satellite constellations offer the advantages of global coverage, wide-area monitoring capability, and continuous monitoring, providing a new solution for global GNSS interference monitoring. This paper provides a comprehensive review of the development history, key methods, system architectures, and future challenges of GNSS interference monitoring technology using LEO satellite constellations.