In this paper, we analyse the conditions and constraints that exist when implementing inquiry-based mathematics education defined and framed by school mathematics curricula. Within the theoretical framework of the anthropological theory of the didactic, we organize our analysis using two main tools. On the one hand, we focus on the external didactic transposition of inquiry in mathematics education. That is, we focus on analysing how the “knowledge to be taught” addresses inquiry, how it is selected, adapted and declared to be taught from international studies to local curriculum reforms. With this purpose in mind, we present an analysis of curricula of four European countries (Denmark, France, Portugal and Spain) to explore which kind of conditions (and constraints) each curriculum establishes for inquiry-based mathematics education. We use the levels of didactic codeterminacy to identify where these conditions and constraints for inquiry come from. It will allow us to compare relevant situations between aforementioned countries.