Algorithmic systems are increasingly used as part of decision-making processes in the public and private sectors, with potentially significant consequences for individuals, organisations and societies. However, the very properties of scale, capability to handle complex datasets, and autonomous learning that make these systems useful also make it difficult to provide clear explanations for the decisions they make. This lack of transparency risks undermining meaningful scrutiny and accountability, which is a significant concern when relating to decision-making processes that can have a considerable impact on fundamental human rights. On the basis of a review of existing proposals for the governance of algorithmic systems, the study offers four sets of policy options, each addressing a different aspect of algorithmic transparency and accountability: i) awareness raising – education, journalism and whistleblowers; ii) accountability in public sector use of algorithmic systems; iii) regulatory oversight and legal liability; and iv) global coordination of algorithmic governance.