The presentation will offer some results of the joint ICMI-ICIAM-study on "Educational Interfaces between Mathematics and Industry (EIMI)", which finished in 2013. Elaborating on Mathematics in these different institutions, it will briefly present the role of Mathematics in these institutions, which are different in terms of different time lines, different goals and different ways to learn. Modelling will be shown as the basic means to bridge the divide between Mathematics and the "rest of the world", using "boundary objects" and "black boxes", which contain and sometimes hide mathematics. Consequences for curricula in Mathematics education and teacher training will be identified.