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Big data introduces challenges to query answering, from theory to practice. A number of questions arise. What queries are "tractable" on big data? How can we make big data "small" so that it is feasible to find exact query answers? When exact answers are beyond reach in practice, what approximation theory can help us strike a balance between the quality of approximate query answers and the costs of computing such answers? To get sensible query answers in big data, what else do we necessarily do in addition to coping with the size of the data? This position paper aims to provide an overview of recent advances in the study of querying big data. We propose approaches to tackling these challenging issues, and identify open problems for future research.