Completeness is a well established concept in physics. It is reflected
in the singularity theorems of Hawking and Penrose. We will give an
overview about the conceptual idea of completeness. The notion of
quantum mechanical completeness is then adapted to situations where
the only adequate description is in terms of quantum field theory in
curved space-times. We will then show that Schwarzschild black holes,
although geodesically incomplete, are quantum complete.
