  The optical conductivity of graphene and bilayer graphene in quantizing
magnetic fields is studied. Both dynamical conductivities, longitudinal and
Hall's, are analytically evaluated. The conductivity peaks are explained in
terms of electron transitions. Correspondences between the transition
frequencies and the magneto-optical features are established using the
theoretical results. The main optical transitions obey the selection rule with
$\Delta n=1$ for the Landau number $n$. The Faraday rotation and light
transmission in the quantizing magnetic fields are calculated. The effects of
temperatures and magnetic fields on the chemical potential are considered.
\pacs{71.20.Nr, 78.20.Ci, 78.20.Bh}
