This chapter examines the theoretical foundations of dependency grammar, a framework that explains sentence structure through direct relations between words rather than constituent-based groupings. Tracing its origins to Tesnière&s;s Éléments de syntaxe structurale, the chapter outlines key concepts such as nucleus, actants, and circonstants, and emphasizes the model&s;s capacity to represent hierarchical relations through dependency trees. Different approaches within dependency grammar are presented, including Word Grammar, Link Grammar, Meaning-Text Theory, the Prague Dependency Treebank, the Universal Dependencies project, Lexical-Functional Grammar, and transition-based models. Each framework is discussed with regard to its theoretical premises, scope of analysis, and contributions to linguistic research and natural language processing. Particular attention is paid to the advantages of dependency-based approaches for languages with flexible word order, such as Turkish, and to their practical applications in fields like machine translation, automatic parsing, sentiment analysis, and information extraction. While acknowledging criticisms related to argument structure and the treatment of morphology, the chapter underscores the enduring relevance of dependency grammar as a bridge between theoretical linguistics and computational applications.