The miniaturization of satellite payloads and the reduction in launch costs have driven the rapid development of Low Earth Orbit (LEO) satellites in the fields of communication, navigation, and remote sensing (CNS), reshaping the industry and global information infrastructure. However, there remain significant challenges and obstacles in the application of LEO satellites within these domains. This paper aims to provide a comprehensive analysis of LEO satellites, with particular emphasis on the development and challenges of communication payloads, to promote further research and applications in these areas. First, the paper examines the evolution of LEO systems and communication payload capabilities from different historical perspectives and user demands. It then explores the opportunities for LEO satellites in the context of global communication infrastructure, particularly in enhancing global connectivity, supporting intelligent transportation through high-precision positioning, navigation, and timing (PNT), and advancing environmental monitoring via passive radar in remote sensing applications. By systematically reviewing the literature on network architectures, medium access control, physical layer technologies, constellation designs, interference management, the application of artificial intelligence, and cost control strategies, this study identifies the major challenges these technologies face in CNS applications. Additionally, the paper discusses future research directions, including large-scale constellations, multi-functional platform integration, advances in intelligence and automation, network convergence and interoperability, interference mitigation, and sustainability. These areas are explored to provide pathways for further technological advancements.