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Dark matter is one of the main mysteries of the modern science. The Standard model of particle physics can not include any new specie of stable particles, thus the existence of DM seems to lead to some ‘New Physics’ scenario. There exists extremely large quantity of SM extensions that could produce DM particles in a very broad mass range. Another option is DM consisting of primordial black holes (PBH)--these objects could be formed at very early stages of the evolution of the Universe and do not need SM extensions. They were formed in rare peaks of overdensity (of order unity) of then horizon size and their masses depend on the time of their formation: the older one has smaller masses. The mass spectrum of PBHs could be very broad indeed--from grams to thousands of solar masses. The main problem in the whole issue of PBH formation is necessity to have huge overdensities which have prohibitively low probability to be realized in the usual inflation senario. Thus we need non-standard spectrum of initial perturbation and/or phase transition that soften the equation of state if we want to form PBHs in any sizable amount. The PBHs are extremely cold and collisionless, but subject to a very slow evaporation (Hawking evaporation). All PBHs with masses smaller than 10^15 g decayed in the lifetime of the Universe, thus they can not comprise DM now. The observational constraints on heavier PBHs comes by means of different methods. The lightest ones (<10^16) could be decaying right now, emitting gamma-rays in abundance. Non-observation of these gamma-rays allow to conclude that PBHs of this mass could contribute only one billionth fraction of whole DM. Heavier PBHs could be ruled out because they would be accumulating inside neutron stars, eventually destroying them; mere existence of NSs allow to constrain PBHs with masses <10^24 g. Still heavier PBHs up to solar masses are severely constrained by various microlensing experiments. Accretion on the heaviest PBHs (<100 000 solar masses) would cause some distortion in the CMB spectrum that are not observed and that effectively rules out PBHs in this mass range as well. Still open window is rather narrow (10^24-10^26 g ) and soon could be tested by ongoing/near future experiments.