Acknowledging the complex relationships which the field of didactics of mathematics has with other research fields (e.g. mathematics, educational sciences, epistemology, history, psychology, semiotics, sociology, cognitive science), the authors analyze in this paper some cases of fruitful and some of failed dialogue between experts of the different fields. They discuss the results of these dialogues, drawing on research studies carried out by the authors, within the paradigm of the Italian research in Mathematics Education.