The ‘accountability revolution’ has lead to an expansion in the concept of accountability and the application of accountability practices to an ever-wider range of public authorities. In a mature democracy, those who exercise significant public power ought to hold themselves open to account, and judicial power should not be excluded from this imperative. In the UK, there are three schools of thought about accountability of judges. ‘Opponents’ argue that the notion of an ‘accountable judge’ is an oxymoron. ‘Re-conceptualists’ point out that courts already engage in a number of practices that make them accountable. The ‘radical’ claim is that new forms of accountability are needed. To understand the debate better, we need to map out types and levels of accountability. First, a distinction may be drawn between the personal accountability of individual judges and the accountability of courts as institutions. Secondly, we may differentiate formal mechanisms for securing accountability and informal, ‘non-state’ practices, including scrutiny of judgments and judges by the news media and academics. Thirdly, different levels of accountability may be identified, relating to the ‘probity’, ‘performance’, ‘process’ and ‘content’ of the judicial function. The final part of the paper considers the design of accountability mechanisms for a new UK Supreme Court.