  Neutron stars are associated with diverse physical phenomena that take place
in conditions characterized by ultrahigh densities as well as intense
gravitational, magnetic, and radiation fields. Understanding the properties and
interactions of matter in these regimes remains one of the challenges in
compact object astrophysics. Photons emitted from the surfaces of neutron stars
provide direct probes of their structure, composition, and magnetic fields. In
this review, I discuss in detail the physics that governs the properties of
emission from the surfaces of neutron stars and their various observational
manifestations. I present the constraints on neutron star radii, core and crust
composition, and magnetic field strength and topology obtained from studies of
their broadband spectra, evolution of thermal luminosity, and the profiles of
pulsations that originate on their surfaces.
