Hawking radiation from dilaton gravity in 1+1 dimensions: a pedagogical review

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.