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