In the past half century, governments have increasingly relied on regulations—secondary legislation issued by administrative bodies and departments—to impose obligations on private parties, multiplying the occasions for regulatory interpretation. This article develops a theory of regulatory interpretation. It argues that such a theory involves understanding the authority of regulations. Turning to the public law of the UK, US, and Australia, this article identifies an intriguing similarity; in each case, regulations have authority when they rationally and nonarbitrarily implement delegated power within the means permitted by statute. The article then argues that this account of regulatory authority justifies a common approach to interpretation in which the object of interpretation is the purpose the regulation seeks to implement, discerned from the regulation's text and accompanying explanation of its purpose, and constrained by background legal norms.