The role of the arbitrator is so significant in the international arbitration that its success or failure may depend on the credibility of the arbitrator. It has long been understood that the ideal arbitrators are should be independent, unbiased, and have the requisite legal and/or technical expertise and experience for the case at hand. Arbitrators may be selected either by agreement of the parties, by appointment by arbitral institution or by a national court. This article outlines the main method of selecting the members of the tribunal plus some of the benefits and burdens of each method. One of the most common methods of appointing arbitrators is by agreement of the parties. This approach is very attractive because it allows parties to submit a their dispute to judges of their own choice, that they also agree on. Most arbitral institutions have a panel of arbitrators and their arbitral rules. So, if disputants agree on a specific arbitral institution, they can settle their disputes by arbitration easily and quickly. If disputants are unable to agree on arbitrator(s) or a specific arbitral institution, method of selecting arbitrator(s) by national court must be employed.