Bearing in mind that there is no uniform solution to the issue of arbitrability of the subject matter of a dispute in international conventions and the Model Law, as well as that different national legislations solve this issue in different ways, the great importance of correctly determining the applicable law for objective arbitrability is noticed. The paper first analyses the lex fori and lex arbitri as classic points of attachment, and then their alternatives such as the lex causae for contract, the place of potential enforcement of the award and the law applicable to the material validity of the arbitration agreement, as well as the proposal to abandon the collision technique. After concluding that for several reasons it is inadequate to apply the law applicable to the arbitration agreement to this issue, and that it is still early to consider that there is an autonomous notion of arbitrability from the New York Convention, the author recognizes that the definition of objective arbitrability encompasses several aspects. Accordingly, for each of them it is necessary to determine separately the applicable law.