The worldwide rollout of 4G LTE mobile communication networks has accelerated the proliferation of the mobile Internet and spurred a new wave of mobile applications on smartphones. This new wave has provided mobile operators an enormous opportunity to collect a huge amount of data to monitor the technical and transactional aspects of their networks. Recent research on mobile big data mining have shown its great potential for diverse purposes ranging from improving traffic management, enabling personal and contextual services, to monitoring city dynamics and so on. The mobile big data research has a multi-disciplinary nature that demands distinct knowledge from mobile communications, signal processing, and data mining. The research field of mobile big data has emerged quickly in recent years, but is somewhat fragmented. This article aims to provide an integrated picture of this emerging field to bridge multiple disciplines and hopefully to inspire future research.