You have already heard about the EEZ, the Exclusive Economic Zone. But what is this zone for? First of all you should know that the size of the EEZ is calculated from the base line onwards and includes 200 miles (= 370 km) around the continental shelf to which each respective countries with riparian rights belongs.
Within its own EEZ each country is allowed to use and mine the mineral and water deposits. Outside of this zone the ocean floor is, as defined by UNESCO, the general heritage of humanity. However, the countries have the possibility to expand their EEZ if certain conditions are fulfilled. It has to be proved that the continental shelf extends beyond these 200 miles/370 km (from the base line). The UN’s Commission on the Limits of the Continental Shelf is responsible for the processing of these cases.
A lot of the suspected resources of the Arctic are outside the EEZ which is why there have been several submissions to the Commission. Besides wanting to extract these resources the countries with riparian rights are also interested in expanding their zone to gain more power in the Arctic.
Source Picture: http://www.nordregio.se/en/Maps–Graphs/07-Cooperation-and-eligible-areas/International-Sea-boundaries-in-the-Arctic/