Big data and its real-world applications have attracted a lot of attention with the explosive growth of data volumes not only in the academic but also in industrial. Big data analysis aimed at mining the potential value of big data has become a popular research topic. Computational intelligence (CI) which is an important research direction of artificial intelligence and information science has been shown to be promising to solve complex problems in scientific research and engineering. CI techniques are expected to provide powerful tools for addressing challenges in big data analytics. This paper surveys the related CI techniques, analyzes the grand challenges brought forth by big data from big data analysis perspectives, and discusses the possible research directions in the future of the big data era. Further, it proposes to conduct the research of big data analysis on scientific big data such as astronomy big data.