In this presentation we use a case study of a recent project to demonstrate how ‘big data’ collected from social media can be used to examine persistent and re-emergent social problems. In this paper we examine anti-vaccination communities online, using data gathered from Facebook and Twitter. Anti-vaccination sentiment has entered public discourse over the past 5 years, boosted by high profile champions such as Jenny McCarthy. Anti-vaccination movements are now persistent and global in scope—utilising social media to create spaces that strengthen, popularise and align anti-vaccination discourses with sympathetic causes and compatible eco-systems of knowledge. Collecting data from Facebook and Twitter allows us to create a broad and detailed picture of the network structure and composition of these online communities and how the discourses within them change and evolve over time. At the same time, analysis of these data are not straightforward. A key challenge is to find and develop computational methods that are attuned to social theory, yet are also capable of engaging with and harnessing the scale and magnitude of big data sets. This paper reports on novel methods that combine natural language processing (NLP) and social network analysis (SNA) to extract insights into the structure and dynamics of the anti-vaccination movement on social media. First, we use conventional SNA methods to examine the structure and composition of anti-vaccination networks, created using Facebook and Twitter data. Next, we leverage NLP techniques to estimate node-level attributes in each network (e.g. the gender of users), as well as edge attributes (e.g. automatically labelling comments and tweets into ‘topics’ using topic modelling). Next, we present a new method for analysing the stability of discourse over time in social media networks. The ‘discourse stability’ method uses set theory to compute how similar the key words are over different time periods, examining comments (Facebook networks) and tweets (Twitter networks). Throughout the paper we report on the preliminary results of these analyses. We conclude with a brief discussion of the challenges and opportunities of new and emerging computational methods for social science research.