The WISDOM (Water Ice Subsurface Deposit Observation on Mars) Ground Penetrating Radar (GPR) is one of the instruments that have been selected as part of the Pasteur payload of ESA's 2018 ExoMars Rover mission. WISDOM main objectives are to understand the geology and evolution of the landing site and to help identifying locations in the shallow subsurface where organic molecules are the most likely to be found and well-preserved. In the context of the ExoMars mission, the importance of the WISDOM GPR is particularly enhanced by its ability to investigate the distribution and state of subsurface water - both as a liquid and as ice. For example, within the diurnally active thermal layer of the subsurface (i.e., the top ~15 - 25 cm), the transient melting and freezing of subsurface ice and brine may be detectable by comparing day- and night-time radar observations at the same location. Moreover, while the biological significance of liquid water on Mars is obvious, a more readily accessible and enduring record of biological activity may be organic biomarkers preserved in subsurface ice. Unfortunately, the dielectric contrast between rock, soil and ice is small, and therefore, differentiating between mixtures of ice-rich and ice-poor regolith in the Martian subsurface is an extraordinarily difficult task. Preliminary tests in both natural (glacier in the Alps and caves in Austria) and artificial (cold chamber) icy environments have been performed with a prototype representative of the WISDOM instrument flight model. These investigations have demonstrated WISDOM's ability to detect and characterize subsurface ice in various forms. Specific examples will be discussed that demonstrate the instrument's depth of sounding, dielectric sensitivity, spatial resolution, full polarimetric and 3-D capability.