This chapter reflects on the notion of parliamentary sovereignty as it is understood in the UK in the light of the Supreme Court's judgment in R (Miller) v Secretary of State for Exiting the European Union, and, more generally, against the backdrop of the UK's membership of the European Union. In particular, in the paper I explore substantive questions about the accommodation of the EU primacy doctrine by the domestic constitutional system and broader questions about the way in which these matters have been dealt with at the level of constitutional theory. In doing so, I pay particular attention to the question whether this episode in UK constitutional history teaches only specific lessons about how EU law has been accommodated — lessons that may be of little if any relevance when or if the UK fully withdraws from the EU — or lessons of a more enduring kind that will remain pertinent long after withdrawal. I argue that it is lessons of the latter type that can be derived from attempts to understand the relationship that has existed this last half-century or so between the domestic and European legal orders. However, I argue too that the extraction of those lessons involves a degree of supposition and inference that speaks volumes about the way in which fundamental constitutional questions are (and are not) confronted in the UK. The UK’s European sojourn is thus revealing, but only to a degree, of the substance of the domestic constitution. And, to the extent that it is less than revealing, the opacity that we encounter serves not simply to obscure the substance but to illuminate something more visceral: namely, a preference that can be discerned within UK constitutional adjudication, at least when it comes to the very biggest questions, for constructive ambiguity over conceptual clarity.