This opinion piece explores the issues of accountability and transparency in relation to the growing use of machine learning algorithms. Citing the recent work of the Royal Society and the British Academy, it looks at the legal protections for individuals afforded by the EU General Data Protection Regulation and asks whether the legal system will be able to adapt to rapid technological change. It concludes by calling for continuing debate that is itself accountable, transparent and public. This article is part of a discussion meeting issue ‘The growing ubiquity of algorithms in society: implications, impacts and innovations'.