© The Author(s) 2015. In this article, we sketch a ‘manifesto’ for the ‘public understanding of big data’. On the one hand, this entails such public understanding of science and public engagement with science and technology-tinged questions as follows: How, when and where are people exposed to, or do they engage with, big data? Who are regarded as big data’s trustworthy sources, or credible commentators and critics? What are the mechanisms by which big data systems are opened to public scrutiny? On the other hand, big data generate many challenges for public understanding of science and public engagement with science and technology: How do we address publics that are simultaneously the informant, the informed and the information of big data? What counts as understanding of, or engagement with, big data, when big data themselves are multiplying, fluid and recursive? As part of our manifesto, we propose a range of empirical, conceptual and methodological exhortations. We also provide Appendix 1 that outlines three novel methods for addressing some of the issues raised in the article.