A review of the achievements of space geodesy in the 21st century, represented by the successful realization of the CHAMP, GOCE, and GRACE missions, is presented. The main result of these missions is the creation of models for the gravitational field of the Earth with high spatial and temporal resolution. In particular, for an uncertainty in the height of the geoid of ~1 mm, the monthly models
... [Show full abstract] contain about 50 spherical harmonics, corresponding to a spatial resolution of ~400 km. The GRACE Follow On mission was launched inMay 2018, whose aim is to provide data for the monthly global models for the gravitational field of the Earth initiated with the GRACE mission. Paths for the development of the next generation of space gravimetry projects are considered. These will enable an appreciable (by no less than a factor of 10) improvement in the precision of models for the gravitational field of the Earth. This paper is based on a presentation made at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).