In 1959, Lucien Tesnière wrote his main work Éléments de syntaxe structurale. While the impact on theoretical linguistics was not very strong at first, 50 years later there exist a variety of linguistic theories based on Tesnière's work. In computational linguistics, as in theoretical linguistics, dependency grammar was not very influential at first. The last 10–15 years, however, have brought a noticeable change and dependency grammar has found its way into computational linguistics. Syntactically annotated corpora based on dependency representations are available for a variety of languages, as well as statistical parsers which give a syntactic analysis of running text describing the underlying dependency relations between word tokens in the text. This article gives an overview of relevant areas of computational linguistics which have been influenced by dependency grammar. It discusses the pros and cons of different types of syntactic representation used in natural language processing and their suitability as representations of meaning. Finally, an attempt is made to give an outlook on the future impact of dependency grammar on computational linguistics.