On 2 April 2012, it was thirty years ago that an armed conflict between Argentina and the UK erupted. The conflict lasted two and a half months and was fought in the South Atlantic region. At the heart of the conflict was the sovereignty dispute over the Falklands-Malvinas. By coincidence or not, a series of events occurred on the eve of the anniversary which has put the dispute once again in the spotlight. The persistence of the dispute over the centuries, the current absence of sovereignty talks between both states while the dispute is heating up, coupled with the earlier 1982 breaches of international peace, make it not only timely but also necessary to revisit the question of the Falklands-Malvinas and to investigate how international law rules and mechanisms could facilitate a peaceful settlement of the dispute. The focus of this article will be on the UN as an international organization established and endowed precisely with the task of facilitating the peaceful settlement of international disputes that are likely to endanger international peace. The article provides a historical record of the UN actions in relation to the question at hand and offers some overarching observations on the adequacy of the UN in facilitating the settlement of territorial disputes.