The present research follows the application of the Law of the Sea for the expansion of the continental shelf, which is becoming increasingly important as technological progress allows the exploration of natural resources in marine areas distant from the coast. By analysing the case of the Brazilian submission to the Commission on the Limits of the Continental Shelf it is possible to understand its function and to know the reasons that led the country to such a choice. The creation of the term Blue Amazon for the area which houses the Brazilian Exclusive Economic Zone and Continental Shelf demonstrates the country's intention to protect economical, environmental, scientific, and national security interests. The research ends by pointing to the progress of the Commission and the positive aspects of the Brazilian submission for the country and the international community.