Despite the critical importance of applicable law in international arbitration, the concept remains misunderstood and often ignored. In the field of international investment law, whether the arbitration proceedings arise from an investment treaty or from a contract, the cornerstone principle of party autonomy applies when it comes to the choice of applicable law, as provided, for example, in article 42 of the ICSID Convention. Even that principle, however, is subject to debate, for example with respect to whether initiating arbitration proceedings under an investment treaty amounts to an implicit choice of applicable law. In an attempt to clarify the notion of applicable law, this contribution first distinguishes the rules of decision, i.e. the law applicable to the specific claims submitted by an investor against a state, from incidentally applicable law, i.e. the other laws which may be relevant for the resolution of the dispute but that do not form a basis for the decision on the merits. In a second part, this contribution analyses several questions arising from the application of choice-of-law provisions in practice, with an emphasis on article 42 of the ICSID Convention. Finally, the consequences of erring in the application of the correct applicable law are examined.