  Cosmology and astroparticle physics give strongest possible evidence for the
incompleteness of the Standard Model of particle physics. Leaving aside
misterious dark energy, which may or may not be just the cosmological constant,
two properties of the Universe cannot be explained by the Standard Model: dark
matter and matter-antimatter asymmtery. Dark matter particles may well be
discovered in foreseeable future; this issue is under intense experimental
investigation. Theoretical hypotheses on the nature of the dark matter
particles are numerous, so we concentrate on several well motivated candidates,
such as WIMPs, axions and sterile neutrinos, and also give examples of less
motivated and more elusive candidates such as fuzzy dark matter. This gives an
idea of the spectrum of conceivable dark matter candidates, while certainly not
exhausting it. We then consider the matter-antimatter asymmetry and discuss
whether it may result from physics at 100~GeV -- TeV scale. Finally, we turn to
the earliest epoch of the cosmological evolution. Although the latter topic
does not appear immediately related to contemporary particle physics, it is of
great interest due to its fundamental nature. We emphasize that the
cosmological data, notably, on CMB anisotropies, unequivocally show that the
well understood hot stage was not the earliest one. The best guess for the
earlier stage is inflation, which is consistent with everything known to date;
however, there are alternative scenarios. We discuss the ways to study the
earliest epoch, with emphasis on future cosmological observations.
