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The idea to generate synthetic data as a tool for broadening access to sensitive microdata has been proposed for the first time three decades ago. While first applications of the idea emerged around the turn of the century, the approach really gained momentum over the last ten years, stimulated at least in parts by some recent developments in computer science. We consider the 30th jubilee of Rubin’s seminal paper on synthetic data (J. Off. Stat. 9 (1993) 462–468) as an opportunity to look back at the historical developments but also to offer a review of the diverse approaches and methodological underpinnings proposed over the years. We will also discuss the various strategies that have been suggested to measure the utility and remaining risk of disclosure of the generated data.