The underlying tension between private autonomy and the principle of state sovereignty in private international law also exists in international arbitration. In principle, all jurisdictions adopting the UNCITRAL Model Law confront international arbitration as a conflict of laws issue. Hence, having in the centre of the analysis the Greek jurisdiction, this article seeks to present and discuss the law applicable to the arbitration agreement, as well as the law applicable to the arbitral procedure (lex arbitrii). A teleological approach of the conflict of laws rules provided for in the UNCITRAL Model Law and the NYC could lead to uniform solutions in all jurisdictions adopting the UNCITRAL Model Law and the NYC.