This article surveys contemporary approaches to international soft law, such as various types of legal positivism, legal realism, critical legal studies, and global administrative law. It scrutinizes to what extent the concept of law endorsed by each of these approaches is able to tackle two challenges caused by the spread of soft law as a means of governance: (1) the fact that international soft law is today often the functional equivalent of international treaties and (2) the contestations of the legitimacy of soft law. It concludes that discursive approaches that stress the public character of international law appear very promising, because they link broad concepts of law with considerations of legitimacy. However, since international institutions today exercise public authority not only through soft law or hard law, but also through non-legal instruments like information, the article argues that one ultimately needs to conceptually dissociate the concept of international law from the concept of public authority.