It is well known that the spectrum condition, i.e. the positivity of the
energy in every inertial coordinate system, is one of the central conceptual
ingredients in model-independent approaches to relativistic quantum field
theory. When one attempts to formulate quantum field theory in a
model-independent manner on a curved background spacetime, it is not
immediately clear which concepts replace the spectrum condition. The present
work is devoted to reviewing facets of this situation, thereby focussing on one
particular approach that attempts to generalize the notion of energy-momentum
spectrum by the notion of "wavefront set", which may be seen as an asymptotic
high-frequency part of the spectrum.