Geophysical techniques were first tested beyond Earth during the Apollo program. Of those examined, radio-wave propagation methods appeared to be the most suitable for the moon and other solar system bodies. This was due to the electromagnetic characteristics of planetary subsurfaces and the possibility to remotely perform measurements on board spacecrafts and rovers. After the first successful experiment on the moon, more than 20 years passed before ground-penetrating radar (GPR) was included in the payload of a planetary mission. Technological advancements in GPR design and successful results of radio echo sounding measurements for the detection of basal water below terrestrial ice sheets paved the way for the application of similar techniques to search for liquid water in the Martian subsurface. Since deployment of the first two subsurface radar sounders above Mars, the number of proposed planetary missions relying on GPR for surveying the subsurface of planets, moons, and other objects has grown progressively. Six orbiting radar sounders and five GPRs mounted on rovers/landers have been employed so far to explore the moon, Mars, and comet 67P/GC. Some of these are in full operation and some are just starting to operate. Planned missions to the icy moons of Jupiter will also depend heavily on radar sounders to detect evidence of an internal ocean on Europa and to understand the habitability conditions on Europa, Ganymede, and Callisto. Finally, planetary missions to Earth's twin, the planet Venus, could take advantage of GPR to understand the cause of its drastic change in climatic conditions and the geologic phenomena that contributed to changing a watery and hospitable surface into a hot and asphyxiating inhabitable planet.