This talk is a short review of part of the searches of new particles of possible interest for Astrophysics
and Cosmology with the different detectors that has been in operation for physics since the year 2010. A consistent
fraction of the efforts of the LHC experiment has been devoted to the search for particle and processes not predicted by the Standard Model that could give some input to the understanding of the nature of the dark matter, but with only limited success until now, specially in the search for evidences in favor of the supersymmetry, that are supposed to be able to explain the large WIMP's abundance observed in the Universe. In the paper are discussed the present status of the searches for WIMPs and rare decays after the Run 1 of LHC, in comparison with the direct and indirect searches for the cosmological relic dark matter, but also the discovery of exotic heavy hadronic states (tetra and pentaquarks), that were hypothesized in QCD many years ago, whose existence appears now convincingly proved.