This contribution presents international judicial institutions as multifunctional actors against the background of a traditional understanding, which sees just one function: settling disputes. The traditional, one-dimensional understanding eclipses other important functions that many international courts do actually perform in contexts of global governance and it underrates problems in their legitimation. In order to appreciate international adjudications’ manifold contributions to social interaction, the paper first identifies three more functions beyond dispute settlement: the stabilization of normative expectations, law-making, and the control as well as legitimation of authority exercised by others. It then places these functions within broader basic understandings of international courts, which respectively picture them as instruments of the parties in a state-centred world order, as organs of a value-based international community, and as institutions of specific legal regimes. The distinct problems that each of these basic understanding faces lead to the contours of a new paradigm for the study of international courts as actors exercising public authority. The present functional analysis ultimately helps to refine both the phenomenon and normative questions.