  The lack of confirmation for the existence of supersymmetric particles and
Weakly Interacting Massive Particles (WIMPs) appeals to extension of the field
of studies of the physical nature of dark matter, involving non-supersymmetric
and non-WIMP solutions. We briefly discuss some examples of such candidates in
their relationship with extension of particle symmetry and pattern of symmetry
breaking. We specify in the example of axion-like particles nontrivial features
of cosmological reflection of the structure and pattern of Peccei-Quinn-like
symmetry breaking. The puzzles of direct and indiect dark matter searches can
find solution in the approach of composite dark matter. The advantages and open
problems of this approach are specified. We note that detailed analysis of
cosmological consequences of any extension of particle model that provides
candidates for dark matter inevitably leads to nonstandard features in the
corresponding cosmological scenario. It makes possible to use methods of
cosmoparticle physics to study physical nature of the dark matter in the
combination of its physical, astrophysical and cosmological signatures.
