Abstract: Detecting cosmic messengers produced by the annihilation/decay of dark matter (DM) gravitationally concentrated in the halo of galaxies and heavy celestial objects has been a major focus for indirect DM searches. In parallel with the search for general signals from the weakly interacting massive particles (WIMPs), alternative DM models can also be searched for with astronomical messengers. In this talk, I will discuss neutrino and gamma-ray signals for inelastic DM annihilating outside neutron stars and probing heavy asymmetric DM whose decay leads to an asymmetry of particle and antiparticle signals with the Glashow resonance. I will conclude with a brief discussion on the prospect of direct detection of the interaction of the cosmic ray-boosted DM in a neutrino telescope.