This Practice Note considers the power of the Cayman Islands courts to stay litigation (or court) proceedings commenced in breach of arbitration agreements in favour of arbitration pursuant to the Arbitration Law 2012. It considers, in summary terms, arbitrability (including of winding-up disputes) and the enforcement of arbitration agreements under Cayman Islands law. The Practice Note also considers the availability of anti-suit injunctions in support of arbitration proceedings under the law of the Cayman Islands. This topic may be referred to as: applying to stay litigation in favour of arbitration; applications to stay court proceedings for arbitration proceedings under Cayman law; approach of Cayman courts to arbitration clauses and agreements; and, ASIs under Cayman Islands law.