  We discuss general Bell inequalities for bipartite and multipartite systems,
emphasizing the connection with convex geometry on the mathematical side, and
the communication aspects on the physical side. Known results on families of
generalized Bell inequalities are summarized. We investigate maximal violations
of Bell inequalities as well as states not violating (certain) Bell
inequalities. Finally, we discuss the relation between Bell inequality
violations and entanglement properties currently discussed in quantum
information theory.
