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Aurora emissions arise when energetic charged particles flowing along highly conducting magnetic field lines excite molecules in the upper atmosphere which returning to the basic state emit energy. At the Earth there are visible auroras and energy for it is taken from the solar wind. The mostly strong field-aligned currents flow at the boundaries between magnetic field lines of different topological types, so the terrestrial auroral oval almost coincides with the open-closed field line boundary in the ionosphere. If in the Earth’s atmosphere, molecules of oxygen and nitrogen take part in the aurora emission process, in Jupiter and Saturn, H and H2 emit UV interacting with the accelerated electrons. This emission is observed by the HST at the Earth orbit. Jupiter’s magnetospheric dynamics is determined by the fast rotation of the planet (~10 h). Due to the highly spinning planet with strong intrinsic magnetic field and due to the magnetospheric sources of the charged particles, a magnetodisc arises inside the jovian magnetosphere. In the inner edge of magnetodisc strong outflow field-aligned currents are generated due to the breakdown of corotation caused by the radial plasma outflow. These field-aligned currents are associated with the main jovian ovals. Auroras at Saturn differ from those at the Earth and Jupiter, in spite of they have similar features from both of them. As at Earth, the shape and size of auroras depend on the solar wind and IMF conditions, and as at Jupiter, some part of emissions are caused by the planetary rotation. Auroras at Saturn are presented by an oval which sometime has a spiral structure and sometime decays on different fragments. The high-latitude boundary of the aurora oval rather well coincides with the open-closed field-line boundary. The almost persistently existing dawn arc maps to closed field lines in the dawn to noon sector, with an outer edge located in the inner part of the ring current, and an inner edge that maps between the centre of the ring current and beyond its outer edge, depending on the latitudinal width of the arc. The dawn arc doesn’t depend on the IMF and is caused by injection of hot plasma from the tail to the dawn sector and corotation breakdown starting from the inner edge of the ring current due to the radial plasma outflow. The temporary existing patchy auroras near to noon and at dusk are straddle the model open-closed field boundary, thus mapping along field lines to the dayside outer magnetosphere and magnetopause and to the tail close to the open-closed boundary. These auroras are associated with reconnection process. For mapping of the bright auroral areas from the ionosphere to the magnetosphere the kronian paraboloid model is used which allows us to receive information about magnetospheric sources of the field-aligned currents generating auroras and to understand mechanisms responsible for it.