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Dark Matter constitutes more that 80% of the total amount of matter in the Universe, yet almost nothing is known about its nature. A powerful investigation technique is that of searching for the products of annihilations of Dark Matter particles in the galactic halo, on top of the ordinary cosmic rays. Recent data from the PAMELA satellite and a number of balloon experiment have reported unexpected excesses in the measured fluxes of cosmic rays. Are these the first direct evidences for Dark Matter? If yes, which DM models and candidates can explain these anomalies and what do they imply for future searches?