This paper takes a sceptical look at the possibility of advanced computer technology replacing judges. Looking first at the example of alternative dispute resolution, where considerable progress has been made in developing tools to assist parties to come to agreement, attention then shifts to evaluating a number of other algorithmic instruments in a criminal justice context. The possibility of human judges being fully replaced within the courtroom strictu sensu is examined, and the various elements of the judicial role that need to be reproduced are considered. Drawing upon understandings of the legal process as an essentially socially determined activity, the paper sounds a note of caution about the capacity of algorithmic approaches to ever fully penetrate this socio-legal milieu and reproduce the activity of judging, properly understood. Finally, the possibilities and dangers of semi-automated justice are reviewed. The risks of seeing this approach as avoiding the recognised problems of fully automated decision-making are highlighted, and attention is directed towards the problems that remain when an algorithmic frame of reference is admitted into the human process of judging.