This article explores the relationships between arbitral tribunals and State courts, between two or more arbitral tribunals, and between State courts in different jurisdictions in relation to the same or related disputes. It reaches three conclusions. First, the broad acceptance of the negative effect of competence-competence ensures a harmonious relationship between the arbitral legal order and the State legal orders, even if the - bilateral - temptation to issue anti-suit injunctions may alter such relationships. Second, the existence of instruments meant to ensure coordination between arbitral tribunals, both in investment arbitration and commercial arbitration, strengthens the idea that arbitration is a true legal order, as opposed to a mere collection of unrelated decisions. Third, the trend found in some jurisdictions to recognize court decisions regarding arbitrations ignores the logic of the New York Convention which invites State courts to exercise control on the award itself, as opposed to focusing on other court decisions ancillary to the award.