Spatial data reconstruction is a process of constructing complete spatial distribution of media attributes based on discrete and sparse point data. Methods based on geostatistics are commonly used in the field of Geosciences. Compressive sensing is a major theoretical breakthrough in the field of signal processing in the 21st century, and has been regarded as a new method of spatial data reconstruction by scholars in the field of Geosciences. This method has achieved good results in static parameter inversion of flow models and the reconstruction of soil mechanical properties. This paper briefly describes mathematical theory of compressive sensing, expounds the research progress of spatial data reconstruction method based on this theory in Geoscience, analyzes the feasibility of this method in spatial data reconstruction of soil characteristics, and puts forward some potential research directions.