Numerical simulations of neutron star-neutron star and neutron star-black
hole binaries play an important role in our ability to model gravitational wave
and electromagnetic signals powered by these systems. These simulations have to
take into account a wide range of physical processes including general
relativity, magnetohydrodynamics, and neutrino radiation transport. The latter
is particularly important in order to understand the properties of the matter
ejected by many mergers, the optical/infrared signals powered by nuclear
reactions in the ejecta, and the contribution of that ejecta to astrophysical
nucleosynthesis. However, accurate evolutions of the neutrino transport
equations that include all relevant physical processes remain beyond our
current reach. In this review, I will discuss the current state of neutrino
modeling in general relativistic simulations of neutron star mergers and of
their post-merger remnants, focusing in particular on the three main types of
algorithms used in simulations so far: leakage, moments, and Monte-Carlo
scheme. I will discuss the advantages and limitations of each scheme, as well
as the various neutrino-matter interactions that should be included in
simulations. We will see that the quality of the treatment of neutrinos in
merger simulations has greatly increased over the last decade, but also that
many potentially important interactions remain difficult to take into account
in simulations (pair annihilation, oscillations, inelastic scattering).
