Under international law, nobody can own the North Pole or the portion of ocean immediately surrounding it, but that doesn’t keep the carving up of the jurisdiction and boundaries of the broader Arctic from being a messy affair: Durham University counts no fewer than twenty different territorial classifications governing the Arctic.
Arctic control is far from a dead, bygone issue:
In August 2007 Russian scientists sent a submarine to the Arctic Ocean seabed at 90° North to gather data in support of Russia’s claim that the North Pole is part of the Russian continental shelf. The expedition provoked a hostile reaction from other Arctic littoral states and prompted media speculation that Russia’s action might trigger a “new Cold War” over the resources of the Arctic.
Hit Durham University’s website for more information and a high-res map (warning: PDF).