Natural language processing supported requirements engineering is an area of research and development that seeks to apply NLP techniques, tools and resources to a variety of requirements documents or artifacts to support a range of linguistic analysis tasks performed at various RE phases. Such tasks include detecting language issues, identifying key domain concepts and establishing traceability links between requirements. This article surveys the landscape of NLP4RE research to understand the state of the art and identify open problems. The systematic mapping study approach is used to conduct this survey, which identified 404 relevant primary studies and reviewed them according to five research questions, cutting across five aspects of NLP4RE research, concerning the state of the literature, the state of empirical research, the research focus, the state of the practice, and the NLP technologies used. Results: 1) NLP4RE is an active and thriving research area in RE that has amassed a large number of publications and attracted widespread attention from diverse communities; 2) most NLP4RE studies are solution proposals having only been evaluated using a laboratory experiment or an example application; 3) most studies have focused on the analysis phase, with detection as their central linguistic analysis task and requirements specification as their commonly processed document type; 4) 130 new tools have been proposed to support a range of linguistic analysis tasks, but there is little evidence of adoption in the long term, although some industrial applications have been published; 5) 140 NLP techniques, 66 NLP tools and 25 NLP resources are extracted from the selected studies.