The total solar irradiance (TSI, or solar constant) acquired a new value: 1361 W m^<-2> instead of 1365 W m^<-2>. However a long-term variation of TSI was not detected. The solar irradiance at the earth's surface is considerably smaller (170 W^<-2>) than previously believed (e.g. 198 W m^<-2> of IPCC AR4). The previous overestimation is due to the underestimation of the absorption of solar radiation in the atmosphere. The absorption of solar radiation in the atmosphere at about 90 W m^<-2>, or 25-28% of the primary solar radiation from space. The global mean atmospheric downward terrestrial radiation is much larger (345 W m^<-2>) than previously assumed (325 W m^<-2> of IPCC AR4). The Arctic has regions of negative annual net radiation, a very rare phenomenon on the globe. These regions are the Central Arctic Ocean with its multi-year ice coverage and the accumulation area of the Greenland ice sheet. The energy balance of these regions is presented. Long-wave incoming radiation has been increasing in the Arctic at a rate of 4-5 W m^<-2>/Decade. The Greenland ice sheet exhibits a large vertical difference in net radiation from the ablation area to the dry snow zone in summer. It ranges from 80 W m^<-2> in the ablation area to 20 W m^<-2> at the equilibrium line and to 10 W m^<-2> in the dry snow zone. This gradient determines the melt gradient on the ice sheet, and is mainly caused by the altitude variation in atmospheric long-wave radiation, seconded by the albedo variation. The effect of albedo in summer for various surfaces is discussed. Simulation capabilities of radiation for many GCMs are investigated.