  The concordance cosmological model based on cold dark matter makes definitive
predictions for the growth of galaxies in the Universe, which are being
actively studied using numerical simulations. These predictions appear to
contradict the observations of dwarf galaxies. Dwarf dark matter halos are more
numerous and have steeper central density profiles than the observed galaxies.
The first of these small-scale problems, the "missing satellites problem", can
be resolved by accounting for the low efficiency of gas cooling and star
formation in dwarf halos. A newly-discovered class of HyperVelocity Stars will
soon allow us to test another generic prediction of CDM models, the triaxial
shapes of dark matter halos. Measuring the proper motions of HVS will probe the
gravitational potential out to 100 kpc and will constrain the axis ratios and
the orientation of the Galactic halo.
