Text simplification, defined narrowly, is the process of reducing the linguistic complexity of a text, while still retaining the original information and meaning. More broadly, text simplification encompasses other operations; for example, conceptual simplification to simplify content as well as form, elaborative modification, where redundancy and explicitness are used to emphasise key points, and text summarisation to omit peripheral or inappropriate information. There is substantial evidence that manual text simplification is an effective intervention for many readers, but automatic simplification has only recently become an established research field. There have been several recent papers on the topic, however, which bring to the table a multitude of methodologies, each with their strengths and weaknesses. The goal of this paper is to summarise the large interdisciplinary body of work on text simplification and highlight the most promising research directions to move the field forward.