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.