  In this contribution we deal with several issues one encounters when trying
to couple quantum matter to classical gravitational fields. We start with a
general background discussion and then move on to two more technical sections.
In the first technical part we consider the question how the Hamiltonian of a
composite two-particle system in an external gravitational field can be
computed in a systematic post-Newtonian setting without backreaction. This
enables us to reliably estimate the consistency and completeness of less
systematic and more intuitive approaches that attempt to solve this problem by
adding `relativistic effects' by hand. In the second technical part we consider
the question of how quantum matter may act as source for classical
gravitational fields via the semiclassical Einstein equations. Statements to
the effect that this approach is fundamentally inconsistent are critically
reviewed.
