  Hawking radiation in d=4 is regarded as a well understood quantum theoretical
feature of Black Holes or of other geometric backgrounds with an event horizon.
On the other hand, the dilaton theory emerging after spherical reduction and
generalized dilaton theories only during the last years became the subject of
numerous studies which unveiled a surprisingly difficult situation. Recently we
have found some solution to the problem of Hawking flux in spherically reduced
gravity which has the merit of using a minimal input. It leads to exact
cancellation of negative contributions to this radiative flux, encountered in
other approaches at infinity, so that our result asymptotically coincides with
the one of minimally coupled scalars. The use of an integrated action is
avoided - although we have been able to present also that quantity in a closed
expression. This short review also summarizes and critically discusses recent
activities in this field, including the problem of ``conformal frames'' for the
background and questions which seem to be open in our own approach as well as
in others.
