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The spacecraft charging is an important factor which gives rise to anomalies in the operation of on-board electronic equipment and damages spacecraft dielectric materials. Two types of spacecraft charging can be considered separately: surface charging, which is caused by hot magnetosphere plasma with electron and proton energy of E 0.1-50 keV, and internal charging of dielectrics due to the influence of electrons of the Earth’s radiation belts with energy of E 1-10 MeV. In general, the main consequence of spacecraft charging are electrostatic discharges that create electromagnetic noise leading to malfunction of on-board electronics and damage spacecraft materials. To study processes of spacecraft charging, computer modeling as well as ground-based and in-flight experiments are carried out. This paper discusses methods of mathematical modeling of spacecraft charging and laboratory experiments to study surface and internal charging, including investigations of electrostatic discharges, and presents the information related to in-flight observations of charging effects on Russian spacecraft in the low-Earth orbits (LEO) and the geostationary orbit (GEO). The Russian spacecraft charging model, COULOMB 2, which was developed in SINP MSU to study surface charging in LEO and GEO, is described, and some calculated electric potential distributions over spacecraft surfaces of GEO and LEO spacecraft under different space conditions are given. The main directions of further research in this field are outlined.