The bulk of these sheets consists of the so-called Polar Layered Deposits, whose characteristic banded appearance is determined by the presence of a different quantity of dust (from a few percent to perhaps 15% or more) in different layers. GPR's mounted aboard ESA's Mars Express and NASA's Mars Reconnaissance Orbiter, named respectively MARSIS and SHARAD, have been probing the PLD's since 2005, providing data on their internal structure down to depths of more than 3.5 km. MARSIS, which operates at frequencies in the MHz range, detected exceptionally strong radar echoes coming from the bottom of the ice sheet in an otherwise featurless part of the South PLD's. These echoes were interpreted as caused by liquid water, whose presence has implications for the study of the climatic and biologic evolution of Mars. The search for subsurface water continues, but it is unlikely that MARSIS will achieve full coverage of the poles before the end of the Mars Express Mission. The SHARAD radar, operating at 20 MHz, does not detect the strong echoes seen by MARSIS, implying a strong dependence on frequency of SPLD radar properties. In this review, the current status of the search for subsurface water will be presented, and the most recent results will be discussed.