Natural language as a modality of interaction is becoming increasingly popular in the field of visualization. In addition to the popular query interfaces, other language-based interactions such as annotations, recommendations, explanations, or documentation experience growing interest. In this survey, we provide an overview of natural language-based interaction in the research area of visualization. We discuss a renowned taxonomy of visualization tasks and classify 119 related works to illustrate the stateof-the-art of how current natural language interfaces support their performance. We examine applied NLP methods and discuss humanmachine dialogue structures with a focus on initiative, duration, and communicative functions in recent visualization-oriented dialogue interfaces. Based on this overview, we point out interesting areas for the future application of NLP methods in the field of visualization.