The non-gravitational nature of dark matter (DM) is one of the most important open questions in modern physics. In this talk, I will try to explore how both astrophysical and cosmological tools can help us in the search for DM. In the first half, I will discuss how Dark matter (DM) particles can get captured inside the Sun due to DM-electron interaction. As the number of these captured DM particles increases, they can annihilate and produce different Standard Model (SM) final states, including neutrinos and anti-neutrinos. Using data-sets from the IceCube neutrino observatory we put the most stringent constraints on DM-electron scattering cross sections in the DM mass range 10 GeV to 10^5 GeV. In the second half, I will show the effects of evaporating primordial black hole (PBH) DM on Intergalactic Medium (IGM) temperature and ionization history. Lyman-alpha forest is a powerful probe of IGM temperature. Using existing Lyman-alpha forest data-sets we put competitive limits on the fraction of DM made up of PBH.