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

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... hysics. 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.