With the proliferation of wireless devices, wireless networks in various forms have become global information infrastructure and an important part of our daily life, which, at the same time, incur fast escalations of both data volumes and energy demand. In other words, energy-efficient wireless networking is a critical and challenging issue in the big data era. In this paper, we provide a comprehensive survey of recent developments on energy-efficient wireless networking technologies that are effective or promisingly effective in addressing the challenges raised by big data. We categorize existing research into two main parts depending on the roles of big data. The first part focuses on energy-efficient wireless networking techniques in dealing with big data and covers studies in big data acquisition, communication, storage, and computation; while the second part investigates recent approaches based on big data analytics that are promising to enhance energy efficiency of wireless networks. In addition, we identify a number of open issues and discuss future research directions for enhancing energy efficiency of wireless networks in the big data era.