Greenwashing is an effort to mislead the public about the environmental impact of an entity, such as a state or company. We provide a comprehensive survey of the scientific literature addressing natural language processing methods to identify potentially misleading climate-related corporate communications, indicative of greenwashing. We break the detection of greenwashing into intermediate tasks, and review the state-of-the-art approaches for each of them. We discuss datasets, methods, and results, as well as limitations and open challenges. We also provide an overview of how far the field has come as a whole, and point out future research directions.