Polarimetry allows sensitivity to the structural and geometric properties of the scene, making it possible a more accurate identification and classification than non-polarimetric systems. Then, polarimetry makes possible new applications, especially in quantitative extraction of bio and geophysical variables. Also, the combination of polarimetry and interferometry allows also to explore the vertical structure of semi-transparent media, like crops and forests. SAR polarimetry is an active field of research in Earth observation. Besides the development of applications, researchers have also focused in theory or physical modelling to make SAR polarimetry an operational technique. This book presents the state of the art in SAR polarimetry, from theory and physical modelling to final applications, but also the current and futures challenges. This book puts also the emphasis on studies for the exploitation of data provided by the new polarimetric space borne SAR sensors, which include additional frequency bands, interferometric capability, enlarged spatial coverage, high spatial resolution and/or shorter revisit times.