This report examines the law on maritime delimitation under the Law of the Sea Convention (LOS Convention) and the maritime boundary dispute between Norway and the Russian Federation in the Barents Sea. Norway and the Russian Federation have been negotiating over the boundaries of their maritime zones in the Barents Sea since the early 1970s. They have failed to agree about the delimitation of the area, except for a relatively small area in the southernmost part of the Barents Sea through the Varanger Fjord Agreement of 1957 and the succeeding Varanger Fjord Agreement of 2007. Norway has argued for the application of a median line delimiting the boundaries, whereas the Russian Federation argues for the application of sector line, leaving a contentious zone between the opposing views of about 175,000 square kilometres. These legal positions will be investigated in light of the historical development of the law on maritime delimitation, as well as recent judgments from the International Court of Justice and other arbitral tribunals since the entering into force of the LOS Convention. In addition, the procedural obligations of Norway and the Russian Federation under the LOS Convention towards finding a solution to their maritime boundary dispute are examined.