  Confronting theoretical models with observations of thermal radiation emitted
by neutron stars is one of the most important ways to understand the properties
of both, superdense matter in the interiors of the neutron stars and dense
magnetized plasmas in their outer layers. Here we review the theory of thermal
emission from the surface layers of strongly magnetized neutron stars, and the
main properties of the observational data. In particular, we focus on the
nearby sources for which a clear thermal component has been detected, without
being contaminated by other emission processes (magnetosphere, accretion,
nebulae). We also discuss the applications of the modern theoretical models of
the formation of spectra of strongly magnetized neutron stars to the observed
thermally emitting objects.
