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. I will focus on the three main types of algorithms
used in simulations so far: leakage, moments, and Monte-Carlo scheme. I will
review 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).
