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