The increasing availability of space-time trajectories left by location-aware devices is expected to enable novel classes of applications where the discovery of consumable, concise, and actionable knowledge is the key step. However, the analysis of mobility data is a critic task by the privacy point of view: in fact, the peculiar nature of location data might enable intrusive inferences in the life of the individuals whose data is analyzed. It is thus important to develop privacy-preserving techniques for the publication and the analysis of mobility data. This chapter provides a brief survey of the research on anonymity preserving data publishing of moving objects databases. While only few papers so far have tackled the problem of anonymity in the off-line case of publication of a moving objects database, rather large body of work has been developed for anonymity on relational data on one side, and for location privacy in the on-line, dynamic context of location based services (LBS), ...