The ‘rule of law’ is a concept at the very heart of the United Nations (UN) mission declared its Secretary-General, Kofi Annan. What does the concept mean internationally? The paper considers its role in international adjudication; in the UN more generally; in terms of the acceptances of the compulsory jurisdiction of the International Court of Justice (ICJ); the difference between thick and thin definitions of the concept; equality before the law; the requirement of clarity and certainty by reference to interpretation of treaties and maritime delimitation; compliance by Governments with international law; and the peaceful settlement of international disputes; and concludes with the importance of personal qualities and professional qualities.