This chapter focuses on the three representations of international arbitration, which attempt to explain which state, or states, provides the relevant source of legitimacy and validity for the arbitration agreement, the arbitral process, and the ensuing award. Under the first representation, the source of legitimacy and validity of arbitration lies in a single national order, that of the seat of the arbitration. The second representation anchors international arbitration in a plurality of national legal orders where recognition or enforcement of an award is sought. Finally, the third representation recognizes an autonomous character to international arbitration, viewed as having generated an authentic and independent legal order: the arbitral legal order. The chapter then explains the basic principles underlying each of the three representations of international arbitration, as well as the consequences of each. It also analyses the evolution of the rules governing the conduct of the arbitral proceeding and the rules applicable to the merits of the dispute from a monolocal view to a transnational view. Despite attempts to deny the existence or convenience of an arbitral legal order, its existence as a transnational legal order—autonomous from all national legal orders—is being increasingly acknowledged.