Social media is becoming an increasingly important data source for learning about breaking news and for following the latest developments of ongoing news. This is in part possible thanks to the existence of mobile devices, which allows anyone with access to the Internet to post updates from anywhere, leading in turn to a growing presence of citizen journalism. Consequently, social media has become a go-to resource for journalists during the process of newsgathering. Use of social media for newsgathering is however challenging, and suitable tools are needed in order to facilitate access to useful information for reporting. In this paper, we provide an overview of research in data mining and natural language processing for mining social media for newsgathering. We discuss five different areas that researchers have worked on to mitigate the challenges inherent to social media newsgathering: news discovery, curation of news, validation and verification of content, newsgathering dashboards, and other tasks. We outline the progress made so far in the field, summarise the current challenges as well as discuss future directions in the use of computational journalism to assist with social media newsgathering. This review is relevant to computer scientists researching news in social media as well as for interdisciplinary researchers interested in the intersection of computer science and journalism.