theoretical basis, but it can be solved by comparing theoretical models with observations of neutron stars. The attempts to solve this long-standing problem by different methods are numerous (e.g., Refs. [@nsb1; @lp07]). Here we discuss current results obtained from studies of cooling isolated neutron stars.

The first papers on neutron star cooling appeared with an advent of X-ray astronomy, before the discovery of neutron stars. Their authors tried to prove that neutron stars cool not too fast and can be discovered as sources of thermal surface X-ray radiation. The first estimates of thermal emission from cooling neutron stars were most probably done by Stabler [@stabler60] in 1960. Four years later Chiu [@chiu64] made similar estimates and analyzed the possibility to discover neutron stars from their thermal emission. First, simplified calculations of neutron star cooling were done in 1964 and 1965 [@morton64; @cs64; @bw65b]. The foundation of the strict cooling theory was laid in 1966 by Tsuruta and Cameron [@tc66], one year before the discovery of pulsars. We review the current state of the cooling theory. More details can be found in recent review papers [@yp04; @pgw06].

Cooling neutron stars
=====================

Neutron stars are thought to consist of a thin crust 