Traditionally, most research in NLP has focused on propositional aspects of meaning. To truly understand language, however, extra-propositional aspects are equally important. Modality and negation typically contribute significantly to these extra-propositional meaning aspects. Although modality and negation have often been neglected by mainstream computational linguistics, interest has grown in recent years, as evidenced by several annotation projects dedicated to these phenomena. Researchers have started to work on modeling factuality, belief and certainty, detecting speculative sentences and hedging, identifying contradictions, and determining the scope of expressions of modality and negation. In this article, we will provide an overview of how modality and negation have been modeled in computational linguistics.