Arbitration is a mode of alternative dispute resolution between natural or legal persons, and it is also a way of resolving disputes between countries. The basis for resolving a dispute in arbitration, which does not include a state body, but an alternative dispute settlement mechanism, is an arbitration agreement between the parties or an arbitration clause in the contract. The subject of the arbitration agreement may be any property claim or a claim in respect of which the parties may settle. Autonomy of the parties in the arbitration proceedings is one of the main features of arbitration, as the procedure is based on the free will of the parties. The decision of the arbitral tribunal, composed of experts, is an arbitral award of which legal effect is equivalent to a final court decision. The arbitral award can be domestic or foreign. Every foreign arbitral award must first be recognized in Slovenia and only then can it be enforced. For the recognition and enforcement of foreign arbitral awards, the Convention on the Recognition and Enforcement of Foreign Arbitral Awards, the so-called New York Convention, has to be applied, to which Article 42 of the Arbitration Act also refers. The procedure for recognition and enforcement is governed by the rules of procedure applicable in the country where recognition is sought. This master's thesis first presents the grounds for refusal which the court verifies on its own motion: the non-arbitrability of the dispute and the violation of public policy of the country in which the procedure for recognition and enforcement of a foreign arbitral award is underway. Thereafter, the grounds for refusal of recognition and enforcement of a foreign arbitral award that may be invoked by a party are detailed, such as: the incapacity of the parties or the invalidity of the arbitration agreement under applicable law, the lack of possibility for the party to participate in the proceedings, the lack of jurisdiction of the arbitral tribunal, the improper composition of the arbitral tribunal, and the invalidity of the arbitral award or its annulment at the place of issue.