We begin by briefly examining the relevance of the study of language in mathematics education research, as well as some of the collaborative forms in which TWG09 is moving the study of language forward in the field. To pro- vide reasons for the recent contributions by TWG09, we summarise lines of concern and tendencies that come from our reading of the set of papers and posters present- ed at CERME9. We build on the review work by Morgan (2013) to argue for the consolidation of such a diversity of lines of concern and tendencies in the contemporary agenda of the domain. The discussion of accomplished goals of the agenda points to a number of challenges and priorities in the context of TWG09 – its participants, their interaction and their activity.