The secure and stable operation of new power systems is essential for supporting the green and low-carbon energy transition and ensuring reliable power supply. With the large-scale integration of high-penetration renewable energy, power-electronics-based equipment, energy storage, and distributed resources, the physical basis for maintaining power-system stability, dynamic mechanisms, analysis methods, and control paradigms have changed substantially. As a result, conventional security and stability analysis and control approaches are becoming difficult to fully adapt to the new situation. conditions. Focusing on the secure and stable operation of new power systems under high penetration renewable energy, this paper develops an overall review framework covering challenge analysis, research framework, and engineering practice. Firstly, the major challenges are summarized from three perspectives: the evolution of the physical basis for stability, modeling and simulation analysis, and the adaptability of stability control. Then, a security and stability control research framework is proposed, centered on a strong physical basis, scientific system operation management, and reliable three lines of defense against disturbances. Based on the explorations and practices of China Southern Power Grid in grid structure optimization, modeling and simulation, stability characteristic analysis, intelligent analysis and computation, coordinated control, and market mechanisms and policy support for security and stability control, the practical implementation path of the security and stability control system for new power systems is summarized. Finally, future development directions are prospected, including online adaptive control, panoramic perception and hybrid simulation, market mechanisms, and coordinated support.