  We describe our recent progress in modeling supernova-fallback disks and
neutron star (NS) atmospheres.
  We present a first detailed spectrum synthesis calculation of a SN-fallback
disk composed of iron. We assume a thin disk with a radial structure described
by the alpha-disk model. The vertical structure and emission spectrum are
computed self-consistently by solving the structure equations simultaneously
with the radiation transfer equations under non-LTE conditions. We describe the
properties of a specific disk model and discuss various effects on the emergent
UV/optical spectrum.
  We investigate Compton scattering effects on the thermal spectrum of NSs. In
addition, we constructed a new generation of metal line-blanketed non-LTE model
atmospheres for NSs. It is compared to X-ray burst spectra of EXO0748-676. It
is possible that the gravitational redshift, deduced from absorption lines, is
lower (z=0.24) than hitherto assumed (z=0.35). Accordingly, this would result
in NS mass and radius lower limits of M>1.63Msun and R>13.8 km.
