The last 5--10 years have seen a massive rise in the popularity of social media platforms such as Twitter, Facebook, Tumblr etc. These platforms enable users to post and share their own content instantly, meaning that material can be seen by multiple others in a short period of time. The growing use of social media has been accompanied by concerns that these platforms enable the rapid and global spread of harmful content. A report by the World Economic Forum puts forward the global risk factor of 'digital wildfires' -- social media events in which provocative content spreads rapidly and broadly, causing significant harm. This provocative content may take the form of rumour, hate speech or inflammatory messages etc. and the harms caused may affect individuals, groups, organisations or populations. In this paper we draw on the World Economic Forum report to ask a central question: does the risk of digital wildfires necessitate new forms of social media governance? We discuss the results of a scoping exercise that examined this central question. Focusing on the UK context, we present short case studies of digital wildfire scenarios and describe four key mechanisms that currently govern social media content. As these mechanisms tend to be retrospective and individual in focus, it is possible that further governance practices could be introduced to deal with the propagation of content proactively and as a form of collective behaviour. However ethical concerns arise over any restrictions to freedom of speech brought about by further governance. Empirical investigation of social media practices and perspectives is needed before it is possible to determine whether new governance practices are necessary or ethically justifiable.