During the last three decades, scientists in formal and natural sciences have been proposing models of language competition. Such models could prove instrumental in informing efforts made towards preserving the world’s linguistic diversity but have yet to gain significant interest among linguists. This situation could be due to a lack of overlap between the concepts and methods used in those models and those used by linguists. In an effort towards promoting interdisciplinary dialogue on the topic of language competition, this study describes the concepts and methods used in mathematical models of language competition and assesses whether these concepts and methods are becoming more similar over time to those used by linguists. To this end, studies that proposed mathematical models of language competition were systematically retrieved and analysed. Change over time in those models was first assessed concerning the way they are specified, including the parameters they contain. Next, it was checked whether models were increasingly fitted to empirical data. Finally, change in the disciplines covered by the journals where those models were published was evaluated. Results show that overall, models have been including few sociolinguistic parameters, have been relying little on empirical data, and have been mostly published in journals covering the fields of mathematics and physics. However, the last years have seen an important turnaround along each of these three axes. A common language seems to be emerging between fields regarding mathematical models of language competition, which should prove instrumental in informing efforts made towards preserving the world’s linguistic diversity.