In the Social Web scenario, large amounts of User-Generated Content (UGC) are diffused through social media often without almost any form of traditional trusted intermediaries. Therefore, the risk of running into misinformation is not negligible. For this reason, assessing and mining the credibility of online information constitutes nowadays a fundamental research issue. Credibility, also referred as believability, is a quality perceived by individuals, who are not always able to discern, with their own cognitive capacities, genuine information from fake one. Hence, in the last years, several approaches have been proposed to automatically assess credibility in social media. Many of them are based on data-driven models, i.e., they employ machine learning techniques to identify misinformation, but recently also model-driven approaches are emerging, as well as graph-based approaches focusing on credibility propagation, and knowledge-based ones exploiting Semantic Web technologies. Three of the main contexts in which the assessment of information credibility has been investigated concern: (i) the detection of opinion spam in review sites, (ii) the detection of fake news in microblogging, and (iii) the credibility assessment of online health-related information. In this article, the main issues connected to the evaluation of information credibility in the Social Web, which are shared by the above-mentioned contexts, are discussed. A concise survey of the approaches and methodologies that have been proposed in recent years to address these issues is also presented.