In the face of rapid global change it is imperative to preserve geodiversity for the overall conservation of biodiversity. Geodiversity is important for understanding complex biogeochemical and physical processes and is directly and indirectly linked to biodiversity on all scales of ecosystem organization. Despite the great importance of geodiversity, there is a lack of suitable monitoring methods. Compared to conventional in-situ techniques, remote sensing (RS) techniques provide a pathway towards cost-effective, increasingly more available, comprehensive, and repeatable, as well as standardized monitoring of continuous geodiversity on the local to global scale. This paper gives an overview of the state-of-the-art approaches for monitoring soil characteristics and soil moisture with unmanned aerial vehicles (UAV) and air- and spaceborne remote sensing techniques. Initially, the definitions for geodiversity along with its five essential characteristics are provided, with an explanation for the latter. Then, the approaches of spectral traits (ST) and spectral trait variations (STV) to record geodiversity using RS are defined. LiDAR (light detection and ranging), thermal and microwave sensors, multispectral, and hyperspectral RS technologies to monitor soil characteristics and soil moisture are also presented. Furthermore, the paper discusses current and future satellite-borne sensors and missions as well as existing data products. Due to the prospects and limitations of the characteristics of different RS sensors, only specific geotraits and geodiversity characteristics can be recorded. The paper provides an overview of those geotraits.