The right usually granted to both parties to appoint one of the arbitrators has often been criticised as one of the elements threatening the legitimacy of investor-state arbitration. However, what is essential is the arbitrators’ impartiality and independence, so that no doubt can be cast on the appropriateness of their work. Rules and recommendations have been formulated with the aim of helping arbitrators retrace their professional and personal life, in order to verify whether there are reasons for not accepting the position, resigning, or disclosing certain information. The paper outlines the criteria governing arbitrators’ appointment procedure, the main situations of conflict, and the behaviours that may give origin to them. This framework provides the point of departure for critical reflections on proposals for amendment of appointment procedures, and the role of soft law in the enhancement of legitimacy of the investor-state arbitration system as a whole.