From smartphones, meters, fridges and cars to internet platforms, the data of digital technologies are the data of citizens. In addition to raising political and ethical issues of privacy, confidentiality and data protection, this calls for rethinking relations to citizens in the production of data for statistics if they are to be trusted by citizens. We outline an approach that involves co-producing data with citizens as partners of statistical production, from the design of a data production platform to the interpretation and analysis of data. While raising issues such as data quality and reliability, we argue co-production can potentially mitigate problems associated with the re-purposing of Big Data. We argue that in a time of “alternative facts”, what constitutes legitimate knowledge and expertise are major political sites of contention and struggle and require going beyond defending existing practices towards inventing new ones. In this context, we contend that the future of official statistics not only depends on inventing new data sources and methods but also mobilising the possibilities of digital technologies to establish new relations with citizens.