Due to global warming, several issues have emerged relating to sea routes and natural resource exploitation directly affecting the coastal states with large stakes in the Arctic. The present thesis begins with a brief history of the Law of the sea and introduces the legal regime of the key maritime zones. It then reviews the demolition of the equidistance method of maritime boundary delimitation with the ICJ judgment on the 1969 North Sea Continental Shelf Cases and describes the three-step approach that followed the jurisdiction of the ICJ, particularly after 2009. At the heart of the thesis lie the rules and procedures regarding the delineation of the outer limits of the continental shelves beyond 200 nm by the coastal states through the illustrating case study of the Arctic region and in particular the Central Arctic Ocean. The reduced ice cover and the potential of natural wealth, which makes the Arctic a new geopolitical hot spot creating overlapping claims among the coastal states concerned, are highlighted to mark the need of determining the final unclarified boundaries in the Arctic Ocean.