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Abstract Negation is a complex linguistic phenomenon present in all human languages. It can be seen as an operator that transforms an expression into another expression whose meaning is in some way opposed to the original expression. In this article, we survey previous work on negation with an emphasis on computational approaches. We start defining negation and two important concepts: scope and focus of negation. Then, we survey work in natural language processing that considers negation primarily as a means to improve the results in some task. We also provide information about corpora containing negation annotations in English and other languages, which usually include a combination of annotations of negation cues, scopes, foci, and negated events. We continue the survey with a description of automated approaches to process negation, ranging from early rule-based systems to systems built with traditional machine learning and neural networks. Finally, we conclude with some reflections on current progress and future directions.