The icy sheet on the surfaces of extraterrestrial bodies and the subsurface ocean environments beneath them have become critical targets for exploring signs of life and habitability. As core tools for penetrating ice layers and reaching subglacial oceans, ice-penetrating probes play an irreplaceable role in future in-situ exploration and represent a key development direction in deep space exploration. This paper systematically reviews the research and development status of deep-space ice-penetrating probes. First, it outlines the progress in detecting subsurface ocean environments in the solar system, focusing on the polar ice caps of Mars and ice moons such as Europa and Enceladus. Second, it summarizes the characteristics of ice-penetrating technologies used on Earth (ice core drills, hot water drills, coiled tubing drills, and ice melters) and their suitability for deep-space missions. This paper then emphasizes the analysis of typical design schemes and research advancements in deep-space ice-penetrating probes from countries including the United States, Germany, Austria, and China. Additionally, key technical challenges are discussed, such as efficient ice penetration, obstacle detection, attitude control, energy supply, information transmission, and planetary protection. In the future, multi-technology integration and innovation will be required to enable ice-penetrating probes to achieve direct detection of extraterrestrial subsurface oceans, thereby providing support for uncovering the origins of life and the evolution of celestial bodies.