  We describe three methods to determine the structure of (sufficiently
continuous) representations of the algebra B^a(E) of all adjointable operators
on a Hilbert B-module E by operators on a Hilbert C-module. While the last and
latest proof is simple and direct and new even for normal representations of
B(H) (H some Hilbert space), the other ones are direct generalizations of the
representation theory of B(H) (based on Arveson's and on Bhat's approaches to
product systems of Hilbert spaces) and depend on technical conditions (for
instance, existence of a unit vector or restriction to von Neumann algebras and
von Neumann modules). We explain why for certain problems the more specific
information available in the older approaches is more useful for the solution
of the problem.
