Big data is on everyone's lips and often raises emotions. On the one hand, the notion is a basis for much technological optimism, mostly directed towards new business models, or simplifications and optimizations in professional and private life. On the other hand, it is a basis for dystopic perspectives, which are targeted, e.g., at profiling of the individual and their privacy space, overarching optimization in daily life and intransparency of decision making. In this article, after a short historical prolog, it is discussed what distinguishes big data from traditional data analysis. The underlying mathematical methods are introduced and scientific successes are reported. Additionally, the risks and limits - especially regarding the derivation of causal relationships - of data analysis are discussed.