  A general overview of the main physical processes driving the cooling of an
isolated neutron star is presented. Among the most important ones are the
various possible neutrino emission processes and the occurrence of baryon
pairing. Special emphasis is also put on the importance of the chemical
composition of the upper layers of the star. A detailed analysis of a Minimal
Scenario, which explicitly postulates that no ``exotic'' form of matter be
present, is summarized and compared with presently available observational
data. No striking incompatibility of the data with the predictions of the
Minimal Scenario is found. Nevertheless, two, possibly three, conspicuous stars
are identified which may, when better data are available, constitute strong
astrophysical evidence for the occurrence of a new state of matter at high
density.
