The explosive growth of data volume and the ever-increasing demands of data value extraction have driven us into the era of big data. The “5V” (Variety, Velocity, Volume, Value, and Veracity) characteristics of big data pose great challenges to traditional computing paradigms and motivate the emergence of new solutions. Cloud computing is one of the representative technologies that can perform massive-scale and complex data computing by taking advantages of virtualized resources, parallel processing and data service integration with scalable data storage. However, as we are also experiencing the revolution of Internet-of-things (IoT), the limitations of cloud computing on supporting lightweight end devices significantly impede the flourish of cloud computing at the intersection of big data and IoT era. It also promotes the urgency of proposing new computing paradigms. We provide an overview on the topic of big data, and a comprehensive survey on how cloud computing as well as its related technologies can address the challenges arisen by big data. Then, we analyze the disadvantages of cloud computing when big data encounters IoT, and introduce two promising computing paradigms, including fog computing and transparent computing, to support the big data services of IoT. Finally, some open challenges and future directions are summarized to foster continued research efforts into this evolving field of study.