Recent measurements of cosmic ray leptons by PAMELA, ATIC, HESS and Fermi revealed interesting excesses. Many authors suggested particle Dark Matter (DM) annihilations could be at the origin of these effects. In this paper, we critically assess this interpretation by reviewing some results questioning the naturalness and robustness of such an interpretation. Natural values for the DM particle parameters lead to a poor leptons production so that models often require signal enhancement effects that we constrain here. Considering DM annihilations are likely to produce antiprotons as well, we use the PAMELA antiproton to proton ratio measurements to constrain a possible exotic contribution. We also consider the possibility of an enhancement due to a nearby clump of DM. This scenario appears unlikely when compared to the state-of-the-art cosmological N-body simulations. We conclude that the bulk of the observed signals most likely has no link with DM and is rather a new, yet unconsidered source of background for searches in these channels.
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