Private international law is often considered and antiquated and formalistic methodology, not particularly relevant for international commercial arbitration. Actually, private international law – in all three its components: conflicts of jurisdiction, conflict of laws and recognition and enforcement of decisions – is crucial to international arbitration. Almost all issues that arise in connection with an international arbitration raise the question of the law under which they are to be solved and, very often, of jurisdiction. This contribution explores the different situations that raise issues of private international law in the context of international arbitration and identifies the most commonly adopted solutions. It also explains that, particularly as regards the applicable law, the rules of private international law applicable before domestic courts are not suitable when conflict of laws issues arise before arbitral tribunals. More generally, the point is made that in many situations the conflict of laws method does not yield satisfactory solutions because, either the relevant conflict rules are not clear, or they designate a national law that often will not contain a specific solution for arbitration. In any case, the conflict of laws method may lead to uncertainty and to a fragmentation of the answers to important arbitration law problems, which is at odds with arbitration’s aspiration to be an international dispute settlement mechanism with a predictable, uniform and non-parochial solutions.