  The hydrogen and helium accreted by X-ray bursting neutron stars is
periodically consumed in runaway thermonuclear reactions that cause the entire
surface to glow brightly in X-rays for a few seconds. With models of the
emission, the mass and radius of the neutron star can be inferred from the
observations. By simultaneously probing neutron star masses and radii, X-ray
bursts are one of the strongest diagnostics of the nature of matter at
extremely high densities. Accurate determinations of these parameters are
difficult, however, due to the highly non-ideal nature of the atmospheres where
X-ray bursts occur. Observations from X-ray telescopes such as RXTE and NuStar
can potentially place strong constraints on nuclear matter once uncertainties
in atmosphere models have been reduced. Here we discuss current progress on
modeling atmospheres of X-ray bursting neutron stars and some of the challenges
still to be overcome.
