Abstract 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 α-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 EXO 0748–676. 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 ⩾ 1.63 M ⊙ and R ⩾ 13.8 km.