Calls emerging from world public opinion for legitimate and effective international institutions require a paradigm shift in public international law. There is a part of public international law that should better be understood as "international public law", because it enables and disciplines the exercise of international public authority, i.e. the pursuit of public interests by international institutions. The paper unfolds our understanding of international public law by way of a thorough discussion of other approaches to governance phenomena in international legal scholarship, including private law approaches, critical approaches, International Institutional Law, Global Administrative Law, and Constitutionalism. It then carves out the notion of international public authority. This notion includes various types of soft and informal governance instruments with innovative compliance mechanisms, as well as the activities of informal and hybrid institutions or network-like structures.