Natural language processing (NLP) technologies are rapidly reshaping how language is created, processed, and analyzed by humans. With current and potential applications in hiring, law, healthcare, and other areas that impact people’s lives, understanding and mitigating harms towards marginalized groups is critical. In this survey, we examine NLP research papers that explicitly address the relationship between LGBTQIA+ communities and NLP technologies. We systematically review all such papers published in the ACL Anthology, to answer the following research questions: (1) What are current research trends? (2) What gaps exist in terms of topics and methods? (3) What areas are open for future work? We find that while the number of papers on queer NLP has grown within the last few years, most papers take a reactive rather than a proactive approach, pointing out bias more often than mitigating it, and focusing on shortcomings of existing systems rather than creating new solutions. Our survey uncovers many opportunities for future work, especially regarding stakeholder involvement, intersectionality, interdisciplinarity, and languages other than English. We also offer an outlook from a queer studies perspective, highlighting understudied topics and gaps in the harms addressed in NLP papers. Beyond being a roadmap of what has been done, this survey is a call to action for work towards more just and inclusive NLP technologies.