This Practice Note considers the impact of the Contract (Right of Third Parties) Act 1999 (C(RTP)A 1999) on arbitration, in particular the established principle that only the parties to the arbitration agreement can be bound by that agreement, participate in the arbitration proceedings and be bound by any resulting arbitral award. The conditional benefit principle is considered. The Practice Note considers the leading cases of Nisshin Shipping Co Ltd v Cleaves and Fortress Value Recovery Fund v Blue Sky Special Opportunities Fund. This topic may be referred to as privity of contract in international arbitration proceedings, the interplay between C(RTP)A 1999 and arbitration, and 3rd parties and arbitration.