The area south of Spitsbergen (about 76°31'N) to latitude 74°N, and between longitudes 10°E and 35°E, by which Svalbard was first defined, contains the small island of Bjørnøya (Bear Island, Bären Insel) and the rest is sea (Fig. 11.1).The 500 m isobath conveniently separates the edge of the Barents shelf from the Norwegian Sea Basin which runs south from Spitsbergen between 14° and 16°30'E. To the east, the large shallow area, Spitsbergenbanken, less than 100 m deep, supports Bjørnøya at its southwestern end, extends northeast to Hopen and joins Edge°ya. It is separated from Spitsbergen to the north by the Storfjordyrenna and to the east by Hopendjupet. These submarine valleys appear to drain westwards into the ocean deep with deltaic fronts convex westward.This chapter focuses first on Bjørnøya which though small is a key outcrop in the Barents Sea and distinct in many respects from Spitsbergen being about 250 km distant. The chapter then surveys a little of what is known of the surrounding sub-sea area.Bjørnøya (20 km N-S and 15 km E-W), as the southern outpost of Svalbard, has long been a key to Svalbard geology since it is generally free all year from tight sea ice. But though its location is convenient, its cliffs generally bar access. Indeed there are very few places where landing by other than inflatable dinghy are feasible. After the island had been claimed by a Norwegian syndicate in 1915 mining of Tournaisian coal began in 1916 and exported over 116000