The meaning of privacy has been much disputed throughout its history in response to wave after wave of new technological capabilities and social configurations. The current round of disputes over privacy fuelled by data science has been a cause of despair for many commentators and a death knell for privacy itself for others. We argue that privacy's disputes are neither an accidental feature of the concept nor a lamentable condition of its applicability. Privacy is essentially contested. Because it is, privacy is transformable according to changing technological and social conditions. To make productive use of privacy's essential contestability, we argue for a new approach to privacy research and practical design, focused on the development of conceptual analytics that facilitate dissecting privacy's multiple uses across multiple contexts.This article is part of the themed issue 'The ethical impact of data science'.