The quantum Boltzmann equations for Fermi-Dirac and Bose-Einstein statistics proposed by Uehling and Uhlembeck (after Nordheim) should be derived from the evolution of real Fermions and Bosons in the so called weak-coupling limit. Since Fokker-Planck-Landau equation is the effective equation associated with a dense and weakly interacting gas of classical particles, it is not surprising that the semi-classical limits of the solutions to quantum Boltzmann equations are expected to be solutions to the Fokker-Planck-Landau equation. In this talk, we will show that these limits can be justified mathematically. It is based on a joint work with Xuguang Lu and Marrio Pulvirenti.