  A brief review is given of the current state of the problem of neutrino pair
emission through neutral weak currents caused by the Cooper pairs breaking and
formation (PBF) in superfluid baryon matter at thermal equilibrium. The cases
of singlet-state pairing with isotropic superfluid gap and spin-triplet pairing
with anisotropic gap are analyzed with allowance for the anomalous weak
interactions caused by superfluidity. It is shown that taking into account the
anomalous weak interactions in both the vector and axial channels is very
important for a correct description of neutrino energy losses through the PBF
processes. The anomalous contributions lead to an almost complete suppression
of the PBF neutrino emission in spin-singlet superfluids and strong reduction
of the PBF neutrino losses in the spin-triplet superfluid neutron matter, which
considerably slows down the cooling rate of neutron stars with superfluid
cores.
