Arbitrators, as individuals or together with other arbitrators as part of an arbitration tribunal, are on a private law basis entrusted to issue a binding award for the parties, which finally resolves their dispute. The paper deals with the appointment of arbitrators and starts from positive and negative requests for their individual appointment. Different modalities of appointing the arbitrators are analyzed, both those arising from the parties' contracts, as well as the mechanisms provided for in the arbitration legislation. An answer is offered to the doubt when choosing between a sole or several arbitrators and their odd or even number. An overview of the qualifications most often expected of arbitrators is provided, followed by a description of their main duties and rights. Finally is the situation of termination of the arbitrator's mandate before the end of the arbitration procedure itself presented, and an insight into the appointment of a substitute arbitrator is given.