The fundamental features of evolution and hydrocarbon potential of the Eurasian continental margin are considered in the light of structure and geological history of major shelf basins whose level of exploration and geodynamic position vary from west to east. The best studied Barents-North Kara Basin is a typical passive margin which borders the Eurasian oceanic opening and displays a prolonged pre-breakup depositional history spanning almost the entire Paleozoic and Mesozoic eras and resulting in a great thickness of sediments with positively proven oil and gas potential. Unique gas condensate fields have also been discovered in the South Kara Basin, although the accumulation of cover sequences did not begin here until about the Paleozoic/Mesozoic time boundary and was probably more influenced by the events in the West Siberian province than in the central Arctic. The location of the Laptev Basin at a unique structural T-junction between continental margin and the Eurasian spreading axis accounts for a specific geodynamic environment leading to post-breakup extension and associated formation of unusually stretched and thinned continental crust beneath a substantial thickness of predominantly latest Mesozoic and Cenozoic sediments. Although the least explored East Siberian and Chukchi Basins represent an apparent morphostructural transition from north-eastern continental Asia to the central Arctic Ocean, their designation as a typical passive margin may, perhaps, be questioned until evolutionary links between the formation of the Amerasian oceanic deep seabed and late Mesozoic - Cenozoic processes of subsidence and sedimentation in eastern basins are established with greater confidence. Because of an outstanding oil and gas potential of the Eurasian continental margin, the fundamental and applied dimensions of its earth science exploration have always been closely interrelated. Of particular interest in a fundamental context are - the examination of the structural and evolutionary continuity between the Eurasian Arctic margin and its neighboring crustal assemblages on both the mainland and the oceanic sides; - unraveling the formation of different parts of this margin in relation to Cenozoic geodynamic processes in the Arctic Ocean; - the issues related to expansion of continental crust in the course of its extensional stretching; - palinspastic reconstructions accounting for the changes in dimensions of continental masses in the course of their pre-and post-breakup evolution, - and studies of deep interior processes causing reorganizations at the upper level of the lithosphere. Among more specific research objectives are - the recognition of syn-oceanic structural elements and tectonic events as opposed to features inherited from the pre-oceanic evolution; - determining the lithostratigraphic composition of the sedimentary cover and developing tectono-stratigraphic concepts for basin modeling; - identifying the factors influencing generation and preservation of hydrocarbons and the criteria for discriminating between predominantly oil-and gas-bearing basins.