  Here we briefly review possible indirect effects of dark matter (DM) of the
Universe. It includes effects in cosmic rays (CR): first of all, the positron
excess at $\sim$ 500 GeV and possible electron-positron excess at 1-1.5 TeV. We
tell that the main and least model-dependent constraint on such possible
interpretation of CR effects goes from gamma-ray background. Even ordinary
$e^+e^-$ mode of DM decay or annihilation produces prompt photons (FSR) so much
that leads to contradiction with data on cosmic gamma-rays. We present our
attempts to possibly avoid gamma-ray constraint. They concern peculiarities of
both space distribution of DM and their physics. The latter involves
complications of decay/annihilation modes of DM, modifications of Lagrangian of
DM-ordinary matter interaction, and inclusion of mode with identical fermions
in final state. In this way, no possibilities to suppress were found except,
possibly, mode with identical fermions. While the case of spatial distribution
variation allows achieving consistency between different data. Also we consider
stable form of dark matter which can interact with baryons. We show which
constraint such DM candidate can get from damping effect in plasma during large
scale structure formation in comparison with other existing constraints.
