The technologies of mobile communications and ubiquitous computing pervade our society, and wireless networks sense the movement of people and vehicles, generating large volumes of mobility data. Miniaturization, wearability, pervasiveness of mobile devices are producing traces of our mobile activity, with increasing positioning accuracy and semantic richness: location data from mobile phones (Global System for Mobile Communications: GSM cell positions), Geographic Positioning System (GPS) tracks from mobile devices receiving geo-positions from satellites, etc. The objective of the GeoPKDD (Geographic Privacy-aware Knowledge Discovery and Delivery), a project funded by European Commission under the Future and emerging technologies (FET) program of the 6th Framework(FP6), has been to discover useful knowledge about human movement behavior from mobility data, while preserving the privacy of the people under observation. Pursuing this ambitious objective, the GeoPKDD project has started a new exciting multidisciplinary research area, at the crossroads of mobility, data mining, and privacy. This paper gives a short overview of the envisaged research challenges and the project achievements.