Tangible climate changes are experienced by the Earth. They refer to long-term changes in, e.g., temperature and precipitation, as well as other aspects of the Earth system. Essential Climate Variables (ECVs) are used to monitor climate changes, validate climate models and, ultimately, inform policy decisions; they are, therefore, essential markers that help scientists understand the Earth system dynamics. As is well known, fundamental contributions to the understanding and characterization of ECV values can be given by the analysis of data produced by current and next-generation missions of Earth observation (EO), which, among other options, can be based on microwave remote sensing. EO sensors can directly characterize bio-geophysical variables connected to ECVs, such as, e.g., the soil moisture (SM), the above-ground biomass (AGB), the freeze-thaw (FT) dynamics of northern latitudes. SM, AGB, and FT are also key variables for the ESA EO science strategy and the ESA Climate Change Initiative program, mainly due to their strong relevance in understanding the global hydrological and carbon cycles. In this work, we perform a comprehensive review about retrieval techniques for SM, AGB, and FT, performed on data collected with passive and active microwave remote sensing sensors. An overview of the methods proposed in the last decades is reported and discussed, then future perspective and current challenges are outlined. This paper targets a very broad scientific community, not necessarily engineers but rather any scientist with interest in microwave EO and satellite remote sensing. For these reason, some basic concepts are briefly reported and discussed throughout the entire manuscript.