He specialized in theoretical astrophysics and radio astronomy, as well as the Sun's corona, supernovae, and cosmic rays and their origins. He showed, in 1946, that the radio-wave radiation from the Sun emanates from the ionized layers of its corona, and he developed a mathematical method for discriminating between thermal and nonthermal radio waves in the Milky Way. He is noted especially for his suggestion that the radiation from the Crab Nebula is due to synchrotron radiation, in which unusually energetic electrons twist through magnetic fields at speeds close to that of light. Shklovsky proposed that cosmic rays from supernova explosions within 300 light years of the sun could have been responsible for some of the mass extinctions of life on earth.