•The study describes the problem of fake news phenomena in digital information.•The study provides a systematic review of the state-of-the-art regarding automatic fake news detection.•From the review, the main subtasks involved in automatic fake news detection are detected and classified.•The review covers systems, resources and competitions in automatic fake news detection.•The review outlines knowledge gaps and future challenges related to automatic fake news detection. Post-truth is a term that describes a distorting phenomenon that aims to manipulate public opinion and behavior. One of its key engines is the spread of Fake News. Nowadays most news is rapidly disseminated in written language via digital media and social networks. Therefore, to detect fake news it is becoming increasingly necessary to apply Artificial Intelligence (AI) and, more specifically Natural Language Processing (NLP). This paper presents a review of the application of AI to the complex task of automatically detecting fake news. The review begins with a definition and classification of fake news. Considering the complexity of the fake news detection task, a divide-and-conquer methodology was applied to identify a series of subtasks to tackle the problem from a computational perspective. As a result, the following subtasks were identified: deception detection; stance detection; controversy and polarization; automated fact checking; clickbait detection; and, credibility scores. From each subtask, a PRISMA compliant systematic review of the main studies was undertaken, searching Google Scholar. The various approaches and technologies are surveyed, as well as the resources and competitions that have been involved in resolving the different subtasks. The review concludes with a roadmap for addressing the future challenges that have emerged from the analysis of the state of the art, providing a rich source of potential work for the research community going forward.