  Direct searches for dark matter lead to serious problems for simple models
with stable neutral Weakly Interacting Massive Particles (WIMPs) as candidates
for dark matter. A possibility is discussed that new stable quarks and charged
leptons exist and are hidden from detection, being bound in neutral dark atoms
of composite dark matter. Stable -2 charged particles $O^{--}$ are bound with
primordial helium in O-helium (OHe) atoms, being specific nuclear interacting
form of composite dark matter. The positive results of DAMA experiments can be
explained as annual modulation of radiative capture of O-helium by nuclei. In
the framework of this approach test of DAMA results in detectors with other
chemical content becomes a nontrivial task, while the experimental search of
stable charged particles at LHC or in cosmic rays acquires a meaning of direct
test for composite dark matter scenario.
