According to the orthodox approach in major arbitration texts, arbitration is considered as operating outside state structures. States consent to arbitration on the basis of the arbitration agreement, and the scope of national court power is inherently restricted by this. In the words of Redfern and Hunter, arbitration is a “private form of justice”, thus outside the public purview of national courts. However, a number of recent cases, in which states have invoked the principle of state immunity in an attempt to exclude the jurisdiction, have given national courts the opportunity to consider the scope of their state’s enforcement jurisdiction (that is, its authority to induce the compliance of parties with the arbitration agreement or arbitral award). Taking into account this practice, this article argues that the orthodox formal consent based approach to authority (i.e. on the basis of the arbitration agreement or under an express provision in national law), according to which national courts only have authority on the basis of the state’s consent to the jurisdiction, overlooks a common and consistent practice in national courts. This practice gives shape to the lawful scope of their enforcement jurisdiction in respect of arbitration proceedings, which is developing irrespective of state consent to their jurisdiction. This practice pertains to three aspects of court authority: supervisory jurisdiction, recognition and enforcement jurisdiction and execution jurisdiction.