  We describe cosmic gamma-ray and neutrino signals of dark matter
annihilation, explaining how the complementarity of these signals provides
additional information that, if observable, can enlighten the particle nature
of dark matter. This is discussed in the context of exploiting the separate
galactic and extragalactic components of the signal, using the spherical halo
model distribution of dark matter. We motivate the discussion with
supersymmetric extensions of the standard model of particle physics. We
consider the minimal supersymmetric standard model (MSSM) where both neutrinos
and gamma-rays are produced from annihilations. We also consider a gauged B-L,
baryon number minus lepton number, extension of the MSSM, where annihilation
can be purely to heavy right-handed neutrinos. We compare the galactic and
extragalactic components of these signals, and conclude that it is not yet
clear which may dominate when looking out of the galactic plane. To answer this
question, we must have an understanding of the contribution of halo
substructure to the annihilation signals. We find that different theories with
indistinguishable gamma-ray signals can be distinguished in the neutrino
signal. Gamma-ray annihilation signals are difficult to observe from the
galactic center, due to abundant astrophysical sources; but annihilation
neutrinos from there would not be so hidden, if they can be observed over the
atmospheric neutrinos produced by cosmic rays.
