We argue that current neutron star observations exclude asymmetric bosonic non-interacting dark matter in the range from 2 keV to 16 GeV, including the 5-15 GeV range favored by DAMA and CoGeNT. If bosonic WIMPs are composite of fermions, the same limits apply provided the compositeness scale is higher than ∼ 10 12 GeV (for WIMP mass ∼ 1 GeV). In case of repulsive self-interactions, we exclude large range of WIMP masses and interaction cross sections which complements the constraints imposed by observations of the Bullet Cluster. Apart from direct searches, constraints on WIMPs can be set by observations of compact objects such as white dwarfs and neutron stars [4][5][6][7][8][9][10][11][12]. These constraints can be grouped in two types. The first type targets WIMPs that can annihilate inside the star producing heat that can change the thermal evolution of the star [5]. WIMPs of this type can arise in supersymmetric extensions of the SM (see [13] and references therein), or in Technicolor models [14]. Constraints of the second type target asymmetric DM models. In these models the annihilation of DM in the present-day Universe is impossible because only particles, and no anti-particles (hence the term "asymmetric") remain [15][16][17][18][19]. An additional bonus in these models is that the asymmetry of WIMPs might be linked through sphalerons with the baryon asymmetry [16,18], which can explain the today's ratio Ω DM /Ω B ∼ 5 provided the WIMP has a mass around 5 GeV. Note that this value is not far from the one suggested by DAMA and CoGeNT. In view of this coincidence, the models with WIMP masses in the GeV range have become quite popular.Since in the asymmetric DM models WIMPs cannot annihilate, if a large number of them is accreted during the lifetime of a neutron star, they may collapse forming a small black hole inside the star that eventually destroy the latter. Therefore the existence of old neutron stars can impose constraints on the properties of asymmetric WIMPs. In fact, in the case of fermionic asymmet-