Recent evaluations suggest that 40% of French pupils enter secondary school with major difficulties in comprehending a written text, whether literary or scientific. Text simplification is a way to make a text more accessible to a given audience. This operation has been of interest to education professionals (teachers, editors) for a long time, but it has recently gained attention in the field of natural language processing. In this article, we summarize the state of the art in the area of text simplification, what is being simplified and how. We propose a typology of linguistic simplifications and we show that text simplification can have a positive effect on reading fluency and comprehension in children with reading difficulties. Finally, we discuss the possibilities and limits of this approach.