Cosmology on small scales

The standard cosmological model LCDM had a remarkable success with predicting and explaining many properties of the Universe. However, it faces difficult challenges on small scales with properties and abundances of dwarf galaxies being the most difficult problems. The situation is confusing and fluent because it involves complicated physics and dynamics of smallest galaxies known, which are difficult to observe. I will give a review of the situation and will discuss possible solution for some of the problems.