Linear Text Segmentation is the task of automatically tagging text documents with topic shifts, i.e. the places in the text where the topics change. A well-established area of research in Natural Language Processing, drawing from well-understood concepts in linguistic and computational linguistic research, the field has recently seen a lot of interest as a result of the surge of text, video, and audio available on the web, which in turn require ways of summarising and categorizing the mole of content for which linear text segmentation is a fundamental step. In this survey, we provide an extensive overview of current advances in linear text segmentation, describing the state of the art in terms of resources and approaches for the task. Finally, we highlight the limitations of available resources and of the task itself, while indicating ways forward based on the most recent literature and under-explored research directions.