This chapter addresses the efforts to enhance the conservation and sustainable use of marine biological diversity in areas beyond national jurisdiction. In particular, it considers the two main areas of contestations, namely the question of the legal regime applicable to marine genetic resources on the deep seabed and the question of the need for conservation measures, including marine protected in areas, in areas beyond national jurisdiction. The first of these issues, the marine genetic resources question, arises from an ambiguity in the UN Convention on the Law of the Sea. It appears a textual reading of the provisions of the Convention. The text of the Convention appears to support neither the contention that the marine genetic resources are governed by the common heritage of mankind principle nor the contention that these resources are governed by the freedom of the high seas. The second area of contestation, the conservation measures question, is concerned with the possible processes and mechanisms to enhance the rudimentary provisions in the Convention. The chapter traces the deliberations over these contested areas within the UN processes, in particular the discussions on the possible need for an implementing agreement to both clarify and expand the provisions of the Convention in relation to marine biological diversity in areas beyond national jurisdiction.