Advancing the deep-sea floating wind power technology is an effective pathway to reducing costs and enhancing efficiency in offshore wind power development, driving structural reforms in the energy system, and achieving the carbon peaking and carbon neutralization vision. Therefore, achieving breakthroughs in core technologies regarding deep-sea floating wind power and accelerating the construction of cost-effective offshore wind power systems have become major tasks in China's energy and electricity fields. This study reviews the development status of deep-sea floating wind power in China and abroad, analyzes the challenges faced by China's deep-sea wind power industry, and explores the key elements for technological breakthroughs in deep-sea floating wind power, involving key scientific issues, core technologies, and basic software capabilities (e.g., integrated coupling design and analysis and real-time digital twin systems). Specifically, the key scientific issues include evolution of aerodynamic loads on wind turbines, motion suppression for semi-submersible foundations, resonance of tension-leg-platform-type foundations, and testing across physical fields. The core technologies include aerodynamic modeling of wind turbines, integrated coupling analysis, structural fatigue analysis, mooring and dynamic cable analysis, load capacity analysis for mooring foundations, advanced material development and testing, large-scale customization of foundation structures, integration and offshore installation and reconnection, and intelligent operation and maintenance (O&M). Additionally, the technical development directions of deep-sea floating wind power technology are elaborated, including different types of floating foundations, overall design of floating wind turbines, independent research and development of key products, core industrial software, efficient construction and installation, and intelligent O&M. Furthermore, it is proposed to establish a technological innovation chain, form an intelligent construction and installation chain, and expand the intelligent O&M system for deep-sea wind power, providing forward thinking for the research and engineering application of the deep-sea floating wind power technology in China.