User stories have been widely accepted as artifacts to capture the user requirements in agile software development. They are short pieces of texts in a semi-structured format that express requirements. Natural language processing (NLP) techniques offer a potential advantage in user story applications. Objective: Conduct a systematic literature review to capture the current state-of-the-art of NLP research on user stories. Method: The search strategy is used to obtain relevant papers from SCOPUS, ScienceDirect, IEEE Xplore, ACM Digital Library, SpringerLink, and Google Scholar. Inclusion and exclusion criteria are applied to filter the search results. We also use the forward and backward snowballing techniques to obtain more comprehensive results. Results: The search results identified 718 papers published between January 2009 to December 2020. After applying the inclusion/exclusion criteria and the snowballing technique, we identified 38 primary studies that discuss NLP techniques in user stories. Most studies used NLP techniques to extract aspects of who, what, and why from user stories. The purpose of NLP studies in user stories is broad, ranging from discovering defects, generating software artifacts, identifying the key abstraction of user stories, and tracing links between model and user stories. Conclusion: NLP can help system analysts manage user stories. Implementing NLP in user stories has many opportunities and challenges. Considering the exploration of NLP techniques and rigorous evaluation methods is required to obtain quality research. As with NLP research in general, the ability to understand a sentence's context continues to be a challenge.