  We review the general construction of distribution functions for gases of
fermions and bosons (photons), emphasizing the similarities and differences
between both cases. The central object which describes polarization for photons
is a tensor-valued distribution function, whereas for fermions it is a
vector-valued one. The collision terms of Boltzmann equations for fermions and
bosons also possess the same general structure and differ only in the quantum
effects associated with the final state of the reactions described. In
particular, neutron-proton conversions in the early universe, which set the
primordial Helium abundance, enjoy many similarities with Compton scattering
which shapes the cosmic microwave background and we show that both can be
handled with a Fokker-Planck type expansion. For neutron-proton conversions,
this allows to obtain the finite nucleon mass corrections, required for precise
theoretical predictions, whereas for Compton scattering it leads to the thermal
and recoil effects which enter the Kompaneets equation. We generalize the
latter to the general case of anisotropic and polarized photon distribution
functions. Finally we discuss a parameterization of the photon spectrum based
on logarithmic moments which allows for a neat separation between temperature
shifts and spectral distortions.
