Fake news detection is a critical yet challenging problem in Natural Language Processing (NLP). The rapid rise of social networking platforms has not only yielded a vast increase in information accessibility but has also accelerated the spread of fake news. Thus, the effect of fake news has been growing, sometimes extending to the offline world and threatening public safety. Given the massive amount of Web content, automatic fake news detection is a practical NLP problem useful to all online content providers, in order to reduce the human time and effort to detect and prevent the spread of fake news. In this paper, we describe the challenges involved in fake news detection and also describe related tasks. We systematically review and compare the task formulations, datasets and NLP solutions that have been developed for this task, and also discuss the potentials and limitations of them. Based on our insights, we outline promising research directions, including more fine-grained, detailed, fair, and practical detection models. We also highlight the difference between fake news detection and other related tasks, and the importance of NLP solutions for fake news detection.