Why and how have languages died out? We have devised a mathematical model to help us understand how languages go extinct. We use the model to ask whether language extinction can be prevented in the future and why it may have occurred in the past. A growing number of mathematical models of language dynamics have been developed to study the conditions for language coexistence and death, yet their phenomenological approach compromises their ability to influence language revitalization policy. In contrast, here we model the mechanisms underlying language competition and look at how these mechanisms are influenced by specific language revitalization interventions, namely, private interventions to raise the status of the language and thus promote language learning at home, public interventions to increase the use of the minority language, and explicit teaching of the minority language in schools. Our model reveals that it is possible to preserve a minority language but that continued long-term interventions will likely be necessary. We identify the parameters that determine which interventions work best under certain linguistic and societal circumstances. In this way the efficacy of interventions of various types can be identified and predicted. Although there are qualitative arguments for these parameter values (e.g., the responsiveness of children to learning a language as a function of the proportion of conversations heard in that language, the relative importance of conversations heard in the family and elsewhere, and the amplification of spoken to heard conversations of the high-status language because of the media), extensive quantitative data are lacking in this field. We propose a way to measure these parameters, allowing our model, as well as others models in the field, to be validated.