In times of budgetary difficulties it is not surprising to see the performance of the public sector questioned. What is surprising is that what is meant by it, and how it is measured, does not seem to matter to either the critics or the advocates of the public sector. The purpose of this chapter is to suggest a definition and a way to measure the performance of the public sector or rather of its main components. Our approach is explicitly rooted in the principles of welfare and production economics. We will proceed in three stages. First of all we present what we call the "performance approach" to the public sector. This concept rests on the principal-agent relation that links a principal, i.e., the public authority, and an agent, i.e., the person in charge of the public sector unit, and on the definition of performance as the extent to which the agent fulfils the objectives assigned to him by the principal. Performance is then measured by using the notion of productive efficiency and of "best practice" frontier technique. We then move to the issue of measuring the productivity of some canonical components of the public sector (railways transportation, waste collection, secondary education and health care). We survey some typical studies of productive efficiency and emphasize the important idea of disentangling conceptual and data problems. This raises the important question that given the available data, does it make sense to assess and measure the productivity of such public sector activities? In the third stage we try to assess the performance of the overall public sector. We argue that for such a level of aggregation one should restrict the performance analysis to the outcomes and not relate it to the resources involved. As an illustration we then turn to an evaluation of the performance of the European welfare states and its evolution over time, using frontier techniques. The results confirm that countries with lowest performance grew faster but this is not sufficient to confirm a path towards convergence.