The evolutionary-genetic method, whereby modern sedimentary basins are interpreted as end-products of a long geological evolution of a system of conjugate palaeo-basins, enables the assessment of the petroleum potential of the Western sector of the Russian Arctic. Modern basins in this region contain relics of palaeo-basins of a certain tectonotype formed in varying geodynamic regimes. Petroleum potential estimates of the Western Arctic vary broadlyfrom 34.7 to more than 100 billion tons of oil equivalent with the share of liquid hydrocarbons from 5.3 to 13.4 billion tons of oil equivalent. At each stage of the development of palaeo-basins, favourable geological, geochemical and thermobaric conditions have emerged and determined the processes of oil and gas formation, migration, accumulation, and subsequent redistribution between different complexes. The most recent stage of basin formation is of crucial importance for the modern distribution of hydrocarbon accumulations. The primary evolutionary-genetic sequence associated with the oil and gas formation regime of a certain type is crucial for the assessment of petroleum potential. Tectonic schemes of individual crustal layers of the Western sector of the Russian Arctic have been compiled based on the interpretation of several seismic data sets. These schemes are accompanied by cross-sections of the Earths crust alongside reference geophysical profiles (geo-traverses). A tectonic scheme of the consolidated basement shows the location and nature of tectonic boundaries of cratons and platform plates with Grenvillian basement as well as Baikalian, Caledonian, Hercynian, and Early Cimmerian fold areas. Four groups of sedimentary basins are distinguished on the tectonic scheme of the platform cover according to the age of its formation: (1) Riphean-Mesozoic on the Early Precambrian basement; (2) Paleozoic-Cenozoic on the Baikalian and Grenvillian basements; (3) Late Paleozoic-Cenozoic on the Caledonian basement; (4) Mesozoic-Cenozoic, overlying a consolidated basement of different ages. Fragments of reference sections along geo-traverses illustrate features of the deep structure of the main geo-structures of the Arctic shelf and continental regions of polar Russia.