Lex arbitri (or ‘law of the arbitration’) is the law applicable to an international arbitration based upon the legal seat designated by the parties. The content of lex arbitri is dictated not by international law, but rather by the national law on international arbitration of the chosen jurisdiction. Typically, lex arbitri will address issues relating to the constitution of the arbitral tribunal and the conduct of the arbitration, including the extent to which local courts may be called upon to assist the arbitration process or may review and enforce any potential award, and the legal limits of arbitration in a jurisdiction.This chapter will consider the impact of lex arbitri on international commercial arbitration on the one hand and international investment treaty arbitration on the other.ICSID investment arbitrations are substantially ‘delocalized’ through the legal framework of the ICSID Convention, reducing their dependency on lex arbitri.By contrast, non-ICSID investment arbitrations are ‘localized’ in the seat of arbitration, and therefore are subject to lex arbitri.The direction of travel of international investment treaty proceedings, shown by complex bespoke procedural regimes in specific IIAs and negotiations for a Multilateral Investment Court, international investment disputes may ultimately ‘graduate’ out of dependence on lex arbitri.