  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 Warmer than Cold dark matter. Slowed down in the terrestrial
matter, OHe is elusive for direct methods of underground dark matter detection
based on the search for effects of nuclear recoil in WIMP-nucleus collisions.
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.
