Big data has begun to significantly influence global production, circulation, distribution, and consumption patterns. It is changing humankind's production methods, lifestyles, mechanisms of economic operation, and country governance models. It is a strategic enabling technology in the era of knowledge-driven economies, and also a new type of strategic resource for nations and the world. It offers a promising new route for innovative methods of analysis and inference, and provides new opportunities for natural sciences, humanities and social sciences. Ubiquitous in the discussion of today's technology, the colorful and not clearly delineated term big data is on people's minds, regarding both its immense potential and its actual and perceived risks. The 6~(th) Exploratory Round Table Conference (ERTC 2015) under the theme of Big Data in the Natural Sciences and Humanities was successfully held in Shanghai in November 2015. It was a joint project of the Chinese Academy of Sciences (CAS) and Max Planck Society (MPG), focused on topics that are only just beginning to emerge in the scientific community. Scientists from CAS and MPG met together with experts around China and the world to review the status of research and technology regarding and using big data and to discuss how it can and should be harnessed for furthering science. Big data is characterized by (1) highly accessible generation of large volumes of data which (2) are generated continuously in a highly dynamic fashion, and which feature (3) high data heterogeneity and (4) serious issues of data quality regarding noise, incompleteness, and biases. The status and requirements of big data research differ substantially among individual scientific domains. In the life sciences, the field has large, internationally shared repositories of highly diverse omics data. Current activities include bringing together biological and medical (patient) data for research on diagnosis and therapy and making patient data accessible while preserving patient privacy. In the Earth sciences, various Earth observation methods, for example, remote sensing, ground sensor networks, geophysics, geochemistry, and geological surveys, have afforded huge volumes of data, so called big Earth data. Exciting themes include global change and digital Earth science. The concept of digital Earth is a virtual representation of our planet constructed with massive, multi-resolution, multi-temporal Earth observation, and socioeconomic data of different types. This multi-disciplinary challenge relies on big data. Big data is also emerging for the humanities and social sciences. High-resolution 3D-imaging, for example, has led to the generation of large amounts of data for digital reproductions of cultural heritage artifacts that require large processing capabilities for filtering and reassembly. The key problem in social sciences is that the vast majority of data is still only available as images, texts, or websites, without appropriate metadata to enable discovery and analysis. Methodologies based on big data pose a number of challenges. (1) In order to gain trust in the data and learned predictive models, the predictions must be interpretable by a human. (2) Another challenge is the resulting loss of privacy: in some settings, complex predictive models are able to recoup partial information from different databases, and effectively deanonymize seemingly anonymous data. (3) At the infrastructure level, energy- and cost-efficient solutions are becoming a growing necessity.