Utilizing Visualization-oriented Natural Language Interfaces (V-NLI) as a complementary input modality to direct manipulation for visual analytics can provide an engaging user experience. It enables users to focus on their tasks rather than worrying about operating the interface to visualization tools. In the past two decades, leveraging advanced natural language processing technologies, numerous V-NLI systems have been developed both within academic research and commercial software, especially in recent years. In this article, we conduct a comprehensive review of the existing V-NLIs. In order to classify each paper, we develop categorical dimensions based on a classic information visualization pipeline with the extension of a V-NLI layer. The following seven stages are used: query understanding, data transformation, visual mapping, view transformation, human interaction, context management, and presentation. Finally, we also shed light on several promising directions for future work in the community.