The concept of party autonomy in arbitration is frequently referred to in the context of the choice of the substantive law or of the applicable rules. While the relationship between parties and arbitrators has been extensively explored, the question of the implications of party autonomy for the process of arbitrator appointments has received less attention. This article submits that the relationship between party autonomy and tribunal appointment also deserves exploration, whether the appointment is undertaken by the parties, by the co-arbitrators, or by various other persons or institutions that act as appointing authorities, since the constitution of the arbitral tribunal reveals the potential vulnerabilities of arbitral awards in the annulment or enforcement process before various state courts. The article also addresses the limits of party autonomy in the appointment of arbitrators and the role of these limits in ensuring that the requisite conditions for fair trial and due process in arbitral proceedings have been met.