Radar sounding is the only remote sensing technique allowing the study of the subsurface of a planet from orbit. By detecting dielectric discontinuities associated with compositional and/or structural discontinuities, it is possible to map the stratigraphy, which can be of fundamental importance to better understand the dynamics and the history of the first meters to kilometers of the subsurface. MARSIS is a synthetic aperture, orbital sounding radar, carried by ESA's Mars Express orbiter. MARSIS is capable of transmitting at four different bands between 1.3 MHz and 5.5 MHz, with a 1 MHz bandwidth.and is optimized for deep penetration, having detected echoes down to a depth of 3.7 km over the South Polar Layered Deposits. MARSIS transmits through a dipole, which has negligible directivity, with the consequence that the radar pulse illuminates the entire surface beneath the spacecraft and not only the near-nadir portion from which subsurface echoes are expected. The electromagnetic wave can then be scattered by any roughness of the surface, and areas that are not directly beneath the radar can scatter part of the incident radiation back towards it, producing surface echoes that will reach the radar after the echo coming from nadir, and that can mask, or be mistaken for, subsurface echoes. The presence of a dispersive medium, such as a plasma, between the radar and its observation target can cause a distortion (dispersion) of the transmitted waveform. Such is the case for Mars, which is surrounded by an atmosphere whose upper layers become ionized and excited through solar radiation, producing an ionosphere. All these effects need to be accounted for and modelled before data can be correctly processed and interpreted. In this talk, various methods used in the analysis of MARSIS data will be presented, and their use demonstrated. Significant results obtained by the radar will be reviewed.