Widespread availability of location aware devices (such as GPS receivers) promotes capture of detailed movement trajectories of people, animals, vehicles and other moving objects, opening new options for a better understanding of the processes involved. In this paper we investigate spatio-temporal movement patterns in large tracking data sets. We present a natural definition of the pattern 'one object is leading others', and discuss how such leadership patterns can be computed from a group of moving entities. The proposed definition is based on behavioural patterns discussed in the behavioural ecology literature. We also present several algorithms for computing the pattern, and they are analysed both theoretically and experimentally.