Seismic and drilling exploration maturity of the Russian Arctic shelf is tens and hundreds of times lower than the exploration maturity of the water areas in the United States of America, Norway, and the United Kingdom. The best studied shelf areas are the southern parts of Barents and Kara seas. The northern Barents and Kara seas and the entire East Arctic shelf (Laptev, East Siberian and Chukchi seas) aren't covered by the parametric drilling. With a limited seismic data, data of gravity and magnetic surveys allowed to outline the main regional structures including sedimentary basins. According to the modern level of geological and geophysical investigation three areas have to be considered as most prospective for the giant oil field discoveries: eastern slope of the North Barents Basin, shelf part of the West Laptev Basin, and southern edge of the North Chukchi Basin.