We review some well-known paradoxes in cosmology and give them a statistical mechanics reading.  Puzzles to be touched include the horizon and the flatness problem, the information paradox, the dark energy problem and the possible origin of the so-called space roar. Each time, we emphasize the role of statistical arguments to complement the dynamical understanding.  Exciting directions for nonequilibrium (statistical) cosmology are briefly added, especially concerning geometric dissipation.