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: location data from mobile phones, GPS tracks from mobile devices receiving geo-positions from satellites, etc. The GeoPKDD project, a large European research initiative, has studied how to discover useful knowledge about human movement behavior from mobility data, while preserving the privacy of the people under observation. A new exciting multidisciplinary research area has thus started, at the crossroads of mobility, data mining, and privacy.