  We briefly review the supersymetric explanation for the cosmic dark matter.
Although the neutralino in the minimal supersymmetric model (MSSM), the
next-to-minimal supersymmetric model (NMSSM) and the nearly minimal
supersymmetric model (nMSSM) can naturaly explain the dark matter relic
density, the PAMELA result can hardly be explained in these popular models. In
the general singlet extension of the MSSM, both the PAMELA result and the relic
density can be explained by the singlino-like neutralino. Such singlino-like
neutralinos annihilate into the singlet-like Higgs bosons, which are light
enough to decay dominantly to muons or electrons, and the annihilation cross
section can be greatly enhanced by the Sommerfeld effect via exchanging a light
CP-even singlet-like Higgs boson. In this scenario, in order to meet the
stringent LEP constraints, the SM-like Higgs boson tends to decay into the
singlet Higgs pairs instead of $b\bar b$ and consequently it will give a
multi-muon signal $h_SM->aa->\mu$ or $h_{SM}->hh->4 a ->8 \mu$ at the LHC.
