Text data can pose a risk of harm. However, the risks are not fully understood, and how to handle, present, and discuss harmful text in a safe way remains an unresolved issue in the NLP community. We provide an analytical framework categorising harms on three axes: (1) the harm type (e.g., misinformation, hate speech or racial stereotypes); (2) whether a harm is sought as a feature of the research design if explicitly studying harmful content (e.g., training a hate speech classifier), versus unsought if harmful content is encountered when working on unrelated problems (e.g., language generation or part-of-speech tagging); and (3) who it affects, from people (mis)represented in the data to those handling the data and those publishing on the data. We provide advice for practitioners, with concrete steps for mitigating harm in research and in publication. To assist implementation we introduce HarmCheck – a documentation standard for handling and presenting harmful text in research.