  Model spectra of neutron star atmospheres are nowadays widely used to fit the
observed thermal X-ray spectra of neutron stars. This fitting is the key
element in the method of the neutronstar radius determination. Here, we present
the basic assumptions used for the neutron star atmosphere modeling as well as
the main qualitative features of the stellar atmospheres leading to the
deviations of the emergent model spectrum from blackbody. We describe the
properties of two of our model atmosphere grids: (i) pure carbon atmospheres
for relatively cool neutron stars (1--4 MK) and (ii) hot atmospheres with
Compton scattering taken into account. The results obtained by applying these
grids to model the X-ray spectra of the central compact object in supernova
remnant HESS 1731-347, and two X-ray bursting neutron stars in low-mass X-ray
binaries, 4U 1724-307 and 4U 1608-52, are presented. Possible systematic
uncertainties associated with the obtained neutron star radii are discussed.
