Deep troughs and ridges of the Arctic Basin are some of the least known features of the Earth's crust. Some of the ridges, eg. Chukchi and Nordwind, are connected directly to the continental shelves and are certainly submarine promontories of the latter. The character of the Lomonosov Ridge as a narrow slice of continental crust that separated from the Eurasian margin in the early Cenozoic (by opening of the Eurasian Basin), is not in doubt. Recent drilling (ACEX) and piston coring have confirmed this interpretation. However there are many other ridges and some of the troughs that are of uncertain origin. Seismic research in combination with potential field data over the East-Siberian margin, Podvodnikov and Makarov basins and the Mendeleev Ridge, presented here, provides a framework for understanding this enigmatic part of the Earth. The constrained models of the crust illustrate their structure. The crust beneath the East Siberian margin is up to 40 km thick; it thins to about 20 km towards to the Podvodnikov Basin. The models over the Arlis Gap, in the middle of the Podvodnikov Basin, and the Mendeleev Ridge have shown that the crust beneath both these features is anomalously thick (up to 28–32 km) and has a velocity structure that suggests the presence of highly attenuated continental crust. The crustal thickness over the Makarov Basin varies from 8 km to 15 km. Reflection profiles provide evidence of the character and thickness of the sedimentary cover (mostly Cenozoic and late Mesozoic), both on the ridges and beneath the troughs. Presented here is evidence that some of the ridges (eg. Marvin Spur) appear to be fragments of continental crust rifted off the Lomonosov Ridge (with a similar, unconformable Cenozoic cover); however, they gently plunge into and beneath troughs (eg. Makarov Basin). Reflection seismic data collected by the HOTRAX expedition in 2005 over the central part of the Lomonosov Ridge illustrate the sedimentary structure on the top of the Ridge and in an internal basin. The main sedimentary units can be interpreted by correlation with the ACEX results. The major fault separating the surrounding ridges from the internal basin appears to have a roll over anticline in the hanging wall, suggesting that the basin was created by a growth fault. The seismic lines provide evidence of gently folded basement beneath the Lomonosov Ridge with intra basement reflections are usually parallel to the upper surfaces; in combination with velocities (c. 4–5 km/s), these suggest the presence of old well-consolidated sediments.