Originally from American Review of International Arbitration - ARIA

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Anti-suit injunctions were originally common-law remedies used to deal with
parallel litigation enjoining one of the parties from pursuing litigation (or
arbitration) in a foreign court (or before an arbitral tribunal).1 Foreign proceedings
may be restrained if they are vexatious or oppressive, but considerations of comity
have relevance in deciding whether to grant an injunction.2 An anti-suit injunction
may be issued by a national court (possibly by an arbitral tribunal)3 to prevent the
principal action from proceeding before another court or tribunal. It is directed at a
party, arbitrator, or arbitral institution4 which it purports to control. More
frequently, an anti-suit injunction attempts to disrupt arbitral proceedings or to
prevent them from being pursued.5 It could therefore be more properly called an
anti-arbitration injunction. Finally, an anti-suit injunction may even be directed at
another anti-suit injunction by a court in another jurisdiction (anti-anti-suitinjunction).6

Although not directed at a foreign court, the remedy is inherently
controversial because it interferes with the foreign parallel litigation. An anti-suit
injunction constitutes an interference by national courts in the arbitration
proceedings. The European Court of Justice ruled in the case of Turner v. Grovit
that an anti-suit injunction is an unjustifiable interference in the process of the
court of a Member State, contrary to the principle of mutual trust underlying the
Brussels Regulation.7