The rapidly growing wave of wireless data service is pushing against the boundary of our communication network's processing power. The pervasive and exponentially increasing data traffic present imminent challenges to all aspects of wireless system design, such as spectrum efficiency, computing capabilities, and fronthaul/backhaul link capacity. In this article, we discuss the challenges and opportunities in the design of scalable wireless systems to embrace the big data era. On one hand, we review the state-of-the-art networking architectures and signal processing techniques adaptable for managing big data traffic in wireless networks. On the other hand, instead of viewing mobile big data as an unwanted burden, we introduce methods to capitalize on the vast data traffic, for building a big-data-aware wireless network with better wireless service quality and new mobile applications. We highlight several promising future research directions for wireless communications in the mobile big data era.