In this paper we first consider alternative measures of efficiency. We explain why simple partial productivity measures are inadequate as the basis of overall measures of efficiency, and outline two alternative approaches. The first is technical efficiency – the degree to which output is maximised for a given level of inputs (or conversely inputs are minimised for a given output) – and the second is cost efficiency, the degree to which costs are minimised for a given level of output. Cost efficiency implies technical efficiency but also allocative efficiency – choosing a cost minimising mix of inputs. We explain why we prefer to measure cost efficiency, both in terms of what governments and regulators are interested in and in terms of practical data problems. We then examine applications of cost function analysis to two areas. The first is rail privatisation in Britain. British experience has seen a large increase in traffic, but also a similar increase in costs. We review attempts to understand and explain both the increase in passenger train operating cost and infrastructure cost using cost function analysis. The second is European rail reform. Countries in Europe have adopted a wide variety of approaches to rail reform, and studies using a mix of European and other countries should be able to shed light on the important question of what works best in different circumstances. Finally we consider how efficiency analysis techniques need to develop in future to address current weaknesses and tackle new challenges.