As the power and sophistication of 'big data' and predictive analytics has continued to expand, so too has policy and public concern about the use of algorithms in contemporary life. This is hardly surprising given our increasing reliance on algorithms in our everyday experience, touching policy sectors from healthcare, transport, finance, retail, manufacturing, education, employment through to public service provision and the operation of the criminal justice system. This has prompted concerns about the need and importance of holding algorithmic power to account, yet it is far from clear that existing legal and other oversight mechanisms are up to the task. This is the introductory chapter to a collection of essays, edited by the authors, offering a critical exploration of 'algorithmic regulation', understood as both a means of coordinating and regulating social action and decision-making, as well as the need for institutional mechanisms through which the power of algorithms and algorithmic systems might themselves be regulated