The planet Mars is the most probable among the terrestrial planets in our solar system to support human settlement or colonization in the future. The detection of water ice or liquid water on the shallow subsurface of Mars is a crucial scientific objective for both the Chinese Tianwen-1 and United States Mars 2020 missions, which were launched in 2020. Both missions were equipped with Rover-mounted ground-penetrating radar (GPR) instruments, specifically the RoPeR on the Zhurong rover and the RIMFAX radar on the Perseverance rover. The in situ radar provides unprecedented opportunities to study the distribution of shallow subsurface water ice on Mars with its unique penetrating capability. The presence of water ice on the shallow surface layers of Mars is one of the most significant indicators of habitability on the extraterrestrial planet. A considerable amount of evidence pointing to the existence of water ice on Mars has been gathered by previous researchers through remote sensing photography, radar, measurements by gamma ray spectroscopy and neutron spectrometers, soil analysis, etc. This paper aims to review the various approaches utilized in detecting shallow subsurface water ice on Mars to date and to sort out the past and current evidence for its presence. This paper also provides a comprehensive overview of the possible clues of shallow subsurface water ice in the landing area of the Perseverance rover, serving as a reference for the RIMFAX radar to detect water ice on Mars in the future. Finally, this paper proposes the future emphasis and direction of rover-mounted radar for water ice exploration on the Martian shallow subsurface.