  The theory of product systems both of Hilbert spaces (Arveson systems) and
product systems of Hilbert modules has reached a status where it seems
appropriate to rest a moment and to have a look at what is known so far and
what are open problems. However, the attempt to give an approximately complete
account in view pages is destined to fail already for Arveson systems since
Tsirelson, Powers and Liebscher have discovered their powerful methods to
construct large classes of examples. In this survey we concentrate on that part
of the theory that works also for Hilbert modules. This does not only help to
make a selection among the possible topics, but it also helps to shed some new
light on the case of Arveson systems. Often, proofs that work for Hilbert
modules also lead to simpler proofs in the case of Hilbert spaces. We put
emphasis on those aspects that arise from recent results about commutants of
von Neumann correspondences, which, in the case of Hilbert spaces, explain the
relation between the Arveson system and the Bhat system associated with an
E_0--semigroup on B(H).
