Coauthors: David Pérez-García (Universidad Complutense de Madrid) Michael M. Wolf (Niels Bohr Institute) Ignacio Villanueva (Universidad Complutense de Madrid) Marius Junge (University of Illinois at Urbana-Champaign)

In this talk we will show how Operator Space Theory appears in the study of Bell Inequalities. We will show the power of this theory by using it to prove the existence of tripartite quantum states which can lead to arbitrarily large violations of Bell Inequalities for dichotomic observables. We will also comment some other results in the framework of general Bell Inequalities, as well as some physical consequences.