The topical problems of the studies in geomagnetism are discussed. A brief outline of the internal and external magnetic field of the Earth is presented; the state of the art of the network magnetic observations including the ground- and space-based measurements is analyzed. The contribution of the Geophysical Center of the Russian Academy of Sciences (GC RAS) in the investigations of the Earth’s magnetic field and development of the national observational segment complying with the highest international quality standards of INTERMAGNET network is demonstrated. The tasks solved by GC RAS in the collection, processing, and analysis of the geomagnetic data are listed. The proposals on updating and improving the system of geomagnetic observations in the Russian Federation are suggested.