‘Big data’ is increasingly being touted as the next big breakthrough in research, business, and government. This option course for the OII MSc in “Social Science of the Internet” moves beyond the hype to critically examine the unprecedented opportunities and serious challenges inherent in big data approaches to advancing knowledge. We start by defining ‘data’ and introducing the social implications of big data research. We then undertake an in depth survey of the empirical literature where big data has been used to address previously unanswerable questions, focusing in particular on social media such as Twitter, mobile phone data and collaboration platforms like Wikipedia. We also compare the approaches taken in a number of different disciplines including economics, literature, and development studies. Finally, we examine the methods used, claims made, and limitations of various approaches in terms of their representativeness and reliability.