  The nonbaryonic dark matter of the Universe is assumed to consist of new
stable particles. A specific case is possible, when new stable particles bear
ordinary electric charge and bind in heavy "atoms" by ordinary Coulomb
interaction. Such possibility is severely restricted by the constraints on
anomalous isotopes of light elements that form positively charged heavy species
with ordinary electrons. The trouble is avoided, if stable particles $X^{--}$
with charge -2 are in excess over their antiparticles (with charge +2) and
there are no stable particles with charges +1 and -1. Then primordial helium,
formed in Big Bang Nucleosynthesis, captures all $X^{--}$ in neutral "atoms" of
O-helium (OHe), thus creating a specific Warmer than Cold nuclear-interacting
composite dark matter. Slowed down in the terrestrial matter, OHe is elusive
for direct methods of underground dark. However OHe-nucleus interaction leads
to their binding and in OHe-Na system the energy of such level can be in the
interval of energy 2-4 keV. It explains the results of DAMA/NaI and DAMA/LIBRA
experiments. The puzzles of direct dark matter searches appear in this solution
as a reflection of nontrivial nuclear physics of OHe. (abridged)
