In recent years, phenomena observed in two quite separate fields of study have led to the suggestion that radio waves may propagate through cold ice masses with sufficiently small loss by absorption to permit the thickness to be measured, and some information about the nature of the bottom surface to be derived by radar. This article describes first some work by the United States Army Signal Research and Development Laboratory arising out of spurious echoes noticed on radio altimeters (ground clearance indicators) carried by aircraft flying in the polar regions. Afterwards it reviews work at the Scott Polar Research Institute where unexpected phenomena on some IGY ionosondes operated in the Antarctic have led to the development of a radio instrument specifically to measure ice thickness.