This position paper investigates the problem of automated text anonymisation, which is a prerequisite for secure sharing of documents containing sensitive information about individuals. We summarise the key concepts behind text anonymisation and provide a review of current approaches. Anonymisation methods have so far been developed in two fields with little mutual interaction, namely natural language processing and privacy-preserving data publishing. Based on a case study, we outline the benefits and limitations of these approaches and discuss a number of open challenges, such as (1) how to account for multiple types of semantic inferences, (2) how to strike a balance between disclosure risk and data utility and (3) how to evaluate the quality of the resulting anonymisation. We lay out a case for moving beyond sequence labelling models and incorporate explicit measures of disclosure risk into the text anonymisation process.