Full-polarimetric Synthetic Aperture Radar (SAR) data contain all the information required to reconstruct the back-scattering mechanism in the signal-target interactions. In space-borne Earth Observation (EO) missions, this allows to successfully characterize the Earth surface and perform more accurate classifications of the land cover and use. On the other hand, the acquisition of full-pol data is very challenging imposing strict constraints over the mission design parameters. Thus, these data result less suitable for extensive EO missions, where the main objective is to provide global coverage at medium spatial and temporal resolution. Indeed, nowadays, current EO SAR missions provide only dual-pol data in their background acquisition mode (e.g. Sentinel-1, PAZ, ICEYE-X). In this seminar, the challenges of extracting polarimetric descriptors of the Earth surface from dual-pol data will be presented, as well as the current solutions and future research directions.