  We present a brief, observational review about the study of the cooling
behaviour of accretion-heated neutron stars and the inferences about the
neutron-star crust and core that have been obtained from these studies.
Accretion of matter during outbursts can heat the crust out of thermal
equilibrium with the core and after the accretion episodes are over, the crust
will cool down until crust-core equilibrium is restored. We discuss the
observed properties of the crust cooling sources and what has been learned
about the physics of neutron-star crusts. We also briefly discuss those systems
that have been observed long after their outbursts were over, i.e, during times
when the crust and core are expected to be in thermal equilibrium. The surface
temperature is then a direct probe for the core temperature. By comparing the
expected temperatures based on estimates of the accretion history of the
targets with the observed ones, the physics of neutron-star cores can be
investigated. Finally, we discuss similar studies performed for strongly
magnetized neutron stars in which the magnetic field might play an important
role in the heating and cooling of the neutron stars.
