Developing the proton exchange membrane (PEM) water electrolysis technology with flexibility in a wider load is an effective pathway to couple renewable energies with water electrolysis for hydrogen production and to achieve renewable energy consumption. This study first reviews scenarios of hydrogen production through the coupling of renewable electricity such as wind and photovoltaic power with fluctuating loads, and analyzes the fluctuation characteristics of renewable energy. Subsequently, it elaborates on the basic characteristics and research progress of water electrolysis for hydrogen production from three aspects: effect of fluctuating power on electrolysis cells, accelerated degradation of electrolysis components, and simulation methods for fluctuating power. Furthermore, the research and development directions of PEM electrolysis cell technology and PEM electrolysis for hydrogen production are explored. The current status and economic feasibility of wind-solar-coupled hydrogen production as well as the industrial application trends of hydrogen production under fluctuating power are clarified. Finally, we propose the following suggestions: (1) deepening the research of fundamental scientific issues and core components of electrolysis cells, (2) further reducing hydrogen production costs, and (3) optimizing the layout of wind-solar-coupled hydrogen production and institutional guarantee.