Languages behave similarly to living species. They display diversity, differentiate in space and time, emerge and disappear. While processes of differentiation happen at a relatively slow rate with a typical timescale of the order of 1,000 years to evolve into different languages, language extinction takes place at a substantially faster rate. Most recent language extinction events are caused by language shift rather than by extinction of the population speaking this language. After providing an overview of the recent literature on modeling language shift with special emphasis on spatial dynamics, the chapter introduces a diffusion-reaction approach and illustrates its usefulness for questions related to revitalization efforts. This approach is, in conclusion, applied to the English-Gaelic language shift situation in Western Scotland and demonstrates what kind of information can be obtained from ematical modeling efforts. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.