Natural language video localization (NLVL), which aims to locate a target moment from a video that semantically corresponds to a text query, is a novel and challenging task. Toward this end, in this paper, we present a comprehensive survey of the NLVL algorithms, where we first propose the pipeline of NLVL, and then categorize them into supervised and weakly-supervised methods, following by the analysis of the strengths and weaknesses of each kind of methods. Subsequently, we present the dataset, evaluation protocols and the general performance analysis. Finally, the possible perspectives are obtained by summarizing the existing methods.