  Dark matter and neutrinos provide the two most compelling pieces of evidence
for new physics beyond the Standard Model of Particle Physics but they are
often treated as two different sectors. The aim of this paper is to determine
whether there are viable particle physics frameworks in which dark matter can
be coupled to active neutrinos. We use a simplified model approach to determine
all possible renormalizable scenarios where there is such a coupling, and study
their astrophysical and cosmological signatures. We find that dark
matter-neutrino interactions have an impact on structure formation and lead to
indirect detection signatures when the coupling between dark matter and
neutrinos is sufficiently large. This can be used to exclude a large fraction
of the parameter space. In most cases, dark matter masses up to a few MeV and
mediator masses up to a few GeV are ruled out. The exclusion region can be
further extended when dark matter is coupled to a spin-1 mediator or when the
dark matter particle and the mediator are degenerate in mass if the mediator is
a spin-0 or spin-1/2 particle.
