  The current status of understanding of the X-ray emission from Seyfert
galaxies involves Comptonization of soft photons by hot subrelativistic
electrons. After briefly reviewing the early theoretical basis for the presence
of hot optically thin plasma in or around accretion disks and the key
observations that led to develop the presently popular model of an accretion
disk with a hot corona, we summarize recent progress in accretion models that
take into account energy dissipation and/or angular momentum transport in the
corona. Finally, adopting the simple scheme of a homogeneous plane parallel
corona, we discuss in detail the dependence of the X-ray spectrum on the
coronal parameters. Despite the strong coupling between optical depth and
temperature which determines a spectral shape insensitive to their precise
values, moderate spectral changes are possible. The spectral variability
patterns can be used as diagnostics for coronal physics and should allow to
determine whether the optical depth of the corona is dominated by e+e- pairs.
