  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.
