We discuss the notion of truth in Mathematics as relative to certain structures, very much in line with Bernays's conception of "bezogene Existenz". Looking to some concrete examples, we argue that even so-called non-standard structures may have their own rationale. As a result, and in accordance with Bourbaki , structures turn out to be tools and have to be judged with respect to their usefulness rather than with respect to a concept of mathematical truth simpliciter.